IS16 Abstracts64 IS16 Abstracts IP1 Nonconformist Image Processing with the Graph Laplacian Operator...

64 IS16 Abstracts

IP1

Nonconformist Image Processing with the GraphLaplacian Operator

The key building blocks of modern image processing aretwo-fold: a measure of affinity between pixels; and an op-erator that turns these affinities into filters that can ac-complish a variety of useful tasks. Examples of the affinitymeasure are many, including bilateral, NLM, etc. And thestandard operator used to construct the filters is the (nor-malized) weighted average of the affinities. But if we con-sider the pixels in an image as nodes in a weighted graph,the Laplacian operator on this graph gives us a strikinglyversatile tool for building a very general class of filters witha much larger range of applications. A little-appreciatedproperty of the (continuous) Laplacian operator is that itmeasures the nonconformity of a function to its surround-ings. This remarkable property and its discrete approxima-tions enable (1) progressive image decomposition from fineto coarse scale, yielding a principled framework for imagesmoothing, sharpening and local tone manipulation; and(2) a clear framework for building image-adapted priors tosolve more general inverse problems such as deblurring. Wehave used this framework to develop many components ofa practical imaging pipeline for mobile and other applica-tions.

Peyman [email protected]

IP2

High Resolution Tactile Sensing for Robotics,Metrology, and Medicine

The interaction of light and matter at a surface is complex.A GelSight sensor overrides the native optics and isolates3D shape. A clear elastomer slab with a reflective mem-brane is pressed against the surface. An embedded cam-era views the membrane; computer vision extracts shape.While conceived as a robot touch sensor, GelSights micron-scale resolution has spawned commercial applications in 3Dsurface metrology (profilometry). In robotics, its high reso-lution, combined with its ability to capture shape, texture,shear, and slip, provides unique tactile capabilities. We arealso exploring medical measurements, ranging from bloodpressure to tissue pathology.

Edward [email protected]

IP3

Image Processing, Internet-of-Things, and In-verse Problems: Blind Deconvolution Meets BlindDemixing

Assume we need to correctly blindly deconvolve and sep-arate (demix) multiple signals at the same time from onesingle received signal. This challenging problem appearsin numerous applications, and is also expected to arise inthe future Internet-of-Things. We will prove that underreasonable assumptions, it is indeed possible to solve thisill-posed inverse problem and recover multiple transmittedfunctions fi and the associated impulse responses gi ro-bustly and efficiently from just one single received signalvia semidefinite programming. We will tip our toes intothe mathematical techniques behind our theory and dis-cuss efficient numerical algorithms as well as applications.

Thomas StrohmerUniversity of California,DavisDepartment of [email protected]

IP4

Semantic Scene Parsing by Entropy Pursuit

The grand challenge of computer vision is to build a ma-chine which produces a rich semantic description of an un-derlying scene based on image data. Mathematical frame-works are advanced from time to time, but none clearlypoints the way to closing the performance gap with nat-ural vision. Entropy pursuit is a sequential Bayesian ap-proach to object detection and localization. The role ofthe prior model is to apply contextual constraints in or-der to determine, and coherently integrate, the evidenceacquired at each step. The evidence is provided by a largefamily of powerful but expensive high-level classifiers (e.g.,CNNs). The order of execution is determined online, and isdriven by removing as much uncertainty as possible aboutthe overall scene interpretation given the evidence to date.The goal is to match, or even exceed, the performance ob-tained with all the classifiers by implementing only a smallfraction.

Donald GemanJohns Hopkins [email protected]

IP5

Recent Advances in Seismic Technology: FromImaging to Inversion

The primary goal of seismic imaging is to transform seismictime reflection data recorded at the earths surface into areflectivity or impedance image of the subsurface in orderto locate hydrocarbon reserves. Historically this has beenaccomplished in seismic processing through imaging algo-rithms that are based on the adjoint of acoustic forwardBorn or Kirchhoff scattering. More recently, however, ad-vances in algorithm development have led to the initial useof nonlinear inversion as an alternative to standard imag-ing algorithms. In this talk I will briefly review the histor-ical development of seismic imaging, and then discuss thestatus of nonlinear inversion in the seismic industry, in-cluding the use of Full-Waveform Inversion for impedancemodel estimation, and more recent tomographic extensionsthat attempt to promote inversion technology into a full-bandwidth model-recovery solution. The various conceptsI present will be illustrated with seismic imaging and inver-sion examples from a number of geologic settings aroundthe world.

Uwe AlbertinChevron Energy Technology [email protected]

IP6

Event-Based Silicon Retina Technology

This talk will be about the development of asynchronoussilicon retina vision sensors that offer a spike-event out-put like biological retinas. These neuromorphic sensorsoffer advantages for real-world vision problems in termsof latency, dynamic range, temporal resolution, and post-processing cost. These event-based sensors offer oppor-

IS16 Abstracts 65

tunities for theoretical and practical developments of newclasses of algorithms aimed at many dynamic vision appli-cations. The presentation will include a demonstration ofa recent-vintage sensor. URL: http://sensors.ini.uzh.ch

Tobi DelbruckUniversity of Zurich and ETH [email protected]

SP1

SIAG/Imaging Science Early Career Prize Lecture- Revisiting Classical Problems of Image Process-ing: Looking for New Ways to Address Longstand-ing Problems

Digital images are generated by using physical acquisitiondevices, such as digital cameras, but also by simulatinglight propagation through environmental models. In bothcases, physical or computational limitations in the imageformation process introduce artifacts such as image bluror noise. Thus, developing image processing techniquesbecomes indispensable to help overcome these barriers. Inthis talk, I present several image processing applicationsin which a change of perspective leads to new insight andsimpler, yet powerful, algorithms. Examples are: intrinsiccamera PSF estimation, burst and video deblurring, MonteCarlo rendering denoising.

Mauricio DelbracioDuke UniversityElectrical & Computer [email protected]

SP2

SIAG/Imaging Science Best Paper Prize Lecture -Scale Invariant Geometry for Nonrigid Shapes

Animals of the same species frequently exhibit local vari-ations in scale. Taking this into account we would like todevelop models and computational tools that answer ques-tions as: How should we measure the discrepancy betweena small dog with large ears and a large one with smallears? Are there geometric structures common to both anelephant and a giraffe? What is the morphometric simi-larity between a blue whale and a dolphin? There havebeen two schools of thoughts that quantified similaritiesbetween surfaces which are insensitive to deformations insize. Namely, scale invariant local descriptors, and globalnormalization methods. Here, we propose a new tool forshape exploration. We introduce a scale invariant met-ric for surfaces that allows us to analyze nonrigid shapes,generate locally invariant features, produce scale invariantgeodesics, embed one surface into another despite changesin local and global size, and assist in the computationalstudy of intrinsic symmetries where the size of a feature isinsignificant.

Yonathan AflaloTechnion [email protected]

Ron KimmelTechnion, Haifa, [email protected]

Dan RavivMIT

[email protected]

CP1

Algorithm to Build A Parametrized Model for theAntenna Aperture Illumination for Radio Astro-nomical Imaging Application

The imaging performance of modern array radio telescopesis limited by the instantaneous knowledge of the time, fre-quency and polarization properties of the antenna apertureillumination pattern (AIP). While imaging algorithms existthat can correct for these effects, they require an accurateinstantaneous model for the antenna AIP. We describe al-gorithm for a low-order parametrized model for the AIPand demonstrate that it captures the dominant time, fre-quency and polarization dependence of the true AIP. Mod-ern interferometric radio telescopes consist of 100s of in-dependent antennas with wide-band receivers (bandwidth8GHz or more) which are together capable of imaging thesky at imaging dynamic range well exceeding a part in amillion. At such high sensitivities the antenna far-fieldpattern varies with time, frequency, polarization. Cor-recting for all these variables of the AIP during imag-ing has so far been considered a hard problem, limitingthe imaging performance of modern radio telescopes. Themethod described here is an important step forward in solv-ing this major problem facing all current and future radiotelescopes for deep-imaging observations. We use a com-putationally efficient ray-tracing code to predict the AIPparametrized for the physical and electromagnetic charac-teristics of the antenna. We show that our method is opti-mal in building an AIP model that minimizes the degrees-of-freedom and demonstrate that without such accuratemodels, modern radio telescopes cannot achieve their ad-vertised imaging performance.

Sanjay BhatnagarNational Radio Astronomy Observatory, Socorro, [email protected]

Preshanth Jagannathan, Walter BriskenNational Radio Astronomy [email protected], [email protected]

CP1

Wide-field full-Stokes Radio Interferometric Imag-ing: The role of the antenna response function

All modern radio interferometry now use wide bandwidthreceives capable of enabling high sensitivity imaging. How-ever such receivers and high sensitivities brings with it anumber of instrumental and atmospheric effects that in-hibit high fidelity, high dynamic range continuum imaging.The dominant instrumental direction dependent effect isthat of the antenna far field voltage pattern. Apart fromtime and frequency dependence, the antenna aperture illu-mination pattern (AIP – Fourier transform of the far-fieldvoltage pattern) also introduces significant instrumentalpolarization in directions away from the center in the field-of-view. To correct for the errors due to all these effects, Ipresent a generalized imaging algorithm that enables deepwide-band imaging of the radio sky in all Stokes. The radiosky is inherently linearly polarized at only a few percentlevel. The full-polarization antenna response to the signalin any one direction is given by the Jones matrix. The di-agonal terms of the Jones matrix encode the antenna gainfor the two incoming pure polarization products (linear orcircular), while the off diagonal terms contains magnitude

66 IS16 Abstracts

of the leakage of one polarization into other due to instru-mental imperfections. In practice these off-diagonal termsare much stronger than the signal making precise measure-ment of sky impossible. The existing A-Projection algo-rithm accounts for only the diagonal terms. In this talk Iwill demonstrate the limitations that arise from ignoringthe off diagonal terms and the need for the generalized A-Projection algorithm. I will then describe the Full-JonesA-Projection algorithm, and show that it will be requiredfor all current and future telescopes to achieve their adver-tised high fidelity, high dynamic range imaging capability.

Preshanth JagannathanNational Radio Astronomy [email protected]

Sanjay BhatnagarNational Radio Astronomy Observatory, Socorro, [email protected]

Urvashi RauNational Radio Astronomy [email protected]

Russ TaylorUniversity of Cape TownUniversity of Western [email protected]

CP1

Effect of Micro-CT Scans Resolution and Scale onthe Prediction of Transport Properties of DigitalRocks

We studied the effects of image resolution on the predictionof transport properties of digital rock samples. Having 3Dmicro-CT scans of Benthein sandstone acquired with dif-ferent resolutions we estimated statistical properties of seg-mented images and performed statistical image reconstruc-tion. After that transport properties and topological struc-ture of the original digital rocks and those reconstructedon the base of truncated Gaussian simulation were com-puted showing that transport properties stabilizes whenresolution goes below 3 micrometers.

Vadim LisitsaInstitute of Petropeum Geology & Geophysics of SB [email protected]

Nadezhda ArefevaNovosibirsk State [email protected]

Yaroslav BazaikinInst. of Mathematics of SB [email protected]

Tatyana KhachkovaInst. of Petroleum Geology and Geophysics SB [email protected]

Dmitriy Kolyukhin(a) Trofimuk Institute of Petroleum Geology andGeophysics

SB RAS Novosibirsk, Russia; (b) Uni CIRP, Bergen,[email protected]

Vladimir TcheverdaInst. of Petroleum Geology and Geophysics SB [email protected]

CP1

Compressive Mid-Infrared Spectroscopic Tomogra-phy: Label Free and Chemically Specific 3D Imag-ing.

We develop a mid-infrared optical imaging modality thatcombines scattering microscopy and imaging spectroscopyto determine spatial morphology and chemical compositionin three spatial dimensions from interferometric data. Theforward imaging model incorporates the constraint that thesample comprises few chemical species with known spec-tra. Images are formed using an iterative reconstructionalgorithm with sparsity-driven regularization. Simulationsillustrate imaging of layered media and sub-wavelengthpoint scatterers in the presence of noise.

Luke PfisterUniversity of Illinois at Urbana [email protected]

Yoram BreslerDepartment of Electrical and Computer Engineering andtheCoordinated Science Laboratory, University of [email protected]

P. Scott CarneyUniversity of Illinois at Urbana [email protected]

CP1

Sparse View Compton Scatter Tomography withEnergy Resolved Data

The use of energy selective detectors for Compton ScatterTomography holds the hope of enhancing the performanceespecially for problems with limited- view in presence ofhighly attenuating materials. We present a broken-ray for-ward model mapping mass density and photoelectrical co-efficients into observed scattered photons, an iterative re-construction method for image formation and initial resultsfor recovering spatial maps of these physical properties tocharacterize material in baggage screening application withlimited view, energy-resolved data.

Hamideh RezaeePhD Candidate, Electrical and Computer EngineeringDepartment, Tufts [email protected]

Brian Tracey, Eric MillerTufts [email protected], [email protected]

CP2

Matrix Decompositions Using Sub-Gaussian Ran-dom Matrices

Matrix decompositions, and especially SVD, are very im-

IS16 Abstracts 67

portant tools in data analysis. When big data is processed,the computation of matrix decompositions becomes expen-sive and impractical. In recent years, several algorithms,which approximate matrix decomposition, have been de-veloped. These algorithms are based on metric conserva-tion features for linear spaces of random projections. Wepresent a randomized method based on sparse matrix dis-tribution that achieves a fast approximation with boundederror for low rank matrix decomposition.

Yariv AizenbudDepartment of Applied Mathematics, School ofMathematicalSciences, Tel Aviv [email protected]

Amir AverbuchSchool of Computer SciencesTel Aviv [email protected]

CP2

Iterated Tikhonov with General Penalty Term

In many applications, such as astronomy and medicine,arises the problem of image deblurring, this inverse prob-lem is ill-conditioned and the inevitable presence of noisemake a very difficult task obtaining a good reconstructionof the true image. The discrete formulation of this problemcomes as a linear system

Ax = b,

where A is a very large and severely ill conditioned matrixand b is corrupted by noise. In order to compute a fairapproximation of the original image the problem has to beregularized. One of the most used regularization methodis Tikhonov regularization

xα = arg minx

‖Ax− b‖2 + α ‖Lx‖2 , α > 0.

The formulation above is called general from, since it in-cludes also the presence of a regularization operator Lwhich weights the penalty term. This operator enhancesome features of the solution while penalizing others. Inthe case L = I , in order to improve the quality of the re-construction, a refinement technique has been introduced.At each step the reconstruction error is approximated us-ing the Tikhonov minimization on the error equation andis used as a correction term, so this algorithm is denoted asIterated Tikhonov. However, to the best of our knowledge,the general theory about this iterative method has beendeveloped only in the standard form, i.e., when L = I . Inthis talk we want to cover the theory behind the generaliterated Tikhonov, when one consider the iteration relatedto Tikhonov minimization in general form. We will formthe method, describe its characteristics and, in particular,we prove that the proposed iteration converges and that isa regularization method. Moreover we will introduce thenon-stationary iterations which will show to be more robustin respect to the choice of the regularization parameter α.Finally, we will show the effectiveness of this method onimage deblurring test data.

Alessandro BucciniUniversita dell’[email protected]

Marco DonatelliUniversity of Insubria

[email protected]

Lothar ReichelKent State [email protected]

CP2

Parallel Douglas Rachford Algorithm for Restor-ing Images with Values in Symmetric HadamardManifolds

The talk addresses a generalization of the Douglas-Rachford algorithm to symmetric Hadamard manifolds. Itcan be used to minimize an anisotropic TV functional forimages having values on these manifolds. We derive anparallel DR algorithm, that can be evaluated fast. Conver-gence of the algorithm to a fixed point is proofed for spaceswith constant curvature. Several numerical examples showits beneficial performance when compared with the cyclicproximal point algorithm or half-quadratic minimization.

Johannes Persch, Ronny Bergmann, Gabriele SteidlUniversity of [email protected],[email protected], [email protected]

CP2

A New Variable Metric Line-Search Proximal-Gradient Method for Image Reconstruction

We present a variable metric line–search based proximal–gradient method for the minimization of the sum of asmooth, possibly nonconvex function plus a convex, pos-sibly nonsmooth term. The strong convergence of themethod can be proved if the objective function satisfiesthe Kurdyka–�Lojasiewicz property at each point of its do-main. Numerical experience on some nonconvex imagereconstruction problems shows the proposed approach iscompetitive with other state-of-the-art methods.

Simone RebegoldiUniversity of Modena and Reggio [email protected]

Silvia BonettiniDipartimento di Matematica e Informatica

Universit{a} di [email protected]

Ignace LorisFNRS Chercheur Qualifie (ULB, Brussels)[email protected]

Federica PortaDipartimento di Matematica e Informatica

Universit{a} di [email protected]

Marco PratoDipartimento di Scienze Fisiche, Informatiche eMatematicheUniversit{a} di Modena e Reggio Emilia

68 IS16 Abstracts

[email protected]

CP2

Modulus Iterative Methods for Nonnegative Con-strained Least Squares Problems Arising from Im-age Restoration

For the solution of large sparse nonnegative constrainedleast squares (NNLS) problems with Tikhonov regulariza-tion arising from image restoration, a new iterative methodis proposed which uses the CGLS method for the inner it-erations and the modulus iterative method for the outeriterations to solve the linear complementarity problemresulted from the Karush-Kuhn-Tucker condition of theNNLS problem. Theoretical convergence analysis includ-ing the optimal choice of the parameter matrix is presentedfor the proposed method. In addition, the method can befurther enhanced by incorporating the active set strategy,which contains two stages where the first stage consists ofmodulus iterations to identify the active set, while the sec-ond stage solves the reduced unconstrained least squaresproblems only on the inactive variables. Numerical exper-iments show the efficiency of the proposed methods com-pared to projection gradient-type methods with less matrixvector multiplications and CPU time.

Ning Zheng

SOKENDAI (The Graduate University for AdvancedStudies)[email protected]

Ken HayamiNational Institute of [email protected]

Junfeng YinDepartment of Mathematics, Tongji University, [email protected]

CP3

Image Deblurring With An Imprecise Blur KernelUsing a Group-Based Low-Rank Image Prior

We present a regularization model for the image deblurringproblem with an imprecise blur kernel degraded by ran-dom errors. In the model, the restored image and blur arecharacterized by a group-based low-rank prior enforcingsimultaneously the nonlocal self-similarity, local sparsity,and mean-preserving properties. An alternating minimiza-tion algorithm is developed to solve the proposed model.Experimental results demonstrate the effectiveness of ourmodel and the efficiency of our numerical scheme.

Tian-Hui Ma, Ting-Zhu Huang, Xi-Le ZhaoSchool of Mathematical SciencesUniversity of Electronic Science and Technology of [email protected], [email protected],[email protected]

Yifei Lou, Yifei LouDepartment of Mathematical SciencesUniversity of Texas at [email protected], [email protected]

CP3

A Fast Algorithm for Structured Low-Rank Matrix

Recovery with Applications to Mri Reconstruction

A powerful new class of MRI reconstruction techniquesrequire solving a large-scale structured low-rank ma-trix recovery problem. We present a novel, fast algo-rithm for this class of problem that adapts an iterativelyreweighted least squares approach to incorporate multi-foldToeplitz/Hankel structures. The iterates can be solved effi-ciently in the original problem domain with few FFTs. Wedemonstrate the algorithm on undersampled MRI recon-struction, which shows significant improvement over stan-dard compressed sensing techniques.

Gregory OngieUniversity of IowaDepartment of [email protected]

Mathews JacobElectrical and Computer EngineeringUniversity of [email protected]

CP3

Enhanced Sparse Low-Rank Matrix Estimation

We propose to estimate sparse low-rank matrices by min-imizing a convex objective function consisting of a data-fidelity term and two non-convex regularizers. The regular-izers induce sparsity of the singular values and the elementsof the matrix, more effectively than the nuclear and the �1norm, respectively. We derive conditions on the regulariz-ers to ensure strict convexity of the objective function. AnADMM based algorithm is derived and is applied to imagedenoising.

Ankit ParekhDepartment of Mathematics, School of EngineeringNew York [email protected]

Ivan SelesnickDepartment of Electrical and Comp. EnggNYU School of [email protected]

CP3

Image Regularization with Structure Tensors -Edge Detection, Filtering, Denoising

Edge detection, filtering, and denoising are fundamentaltopics in digital image and video processing area. Edgepreserving regularization and diffusion based methods al-though extensively studied and widely used for imagerestoration, still have limitations in adapting to local struc-tures. We consider a class of filters based on multiscalestructure tensor based features. The spatially varyingexponent model we develop leads to a novel restorationmethod which retains and enhances edge structures acrossscales without generating artifacts. Promising extensionsto handle jpeg decompression, edge detection, and multi-channel imagery are considered. Related project page con-tains more details: http://cell.missouri.edu/pages/MTTV.

Surya PrasathUniversity of [email protected]

Dmitry A. Vorotnikov

IS16 Abstracts 69

Universidade de [email protected]

Rengarajan Pelapur, Shani JoseUniversity of Missouri-Columbia, [email protected], [email protected]

Kannappan PalaniappanUniversity of [email protected]

Guna SeetharamanNavy Research Lab, [email protected]

CP3

Signal Classification Using Sparse Representationon Enhanced Training Dictionary

We propose a method to classify high-dimensional signalsbased on how sparsely a test signal can be represented overa dictionary containing selected training samples and basisvectors of the approximated tangent planes at those train-ing samples, which are computed using local PCA. Our ex-periments on various datasets including the standard facedatabases demonstrate that this method can achieve higherclassification accuracy than other sparse representation-based methods when the class manifolds are nonlinear andsparsely-sampled.

Naoki SaitoDepartment of MathematicsUniversity of California, [email protected]

Chelsea WeaverUniversity of California, [email protected]

CP3

Low-Rank Approximation Pursuit for Matrix andTensor Completion

we introduce an efficient greedy algorithm for matrix com-pletion, which is literally a generalization of orthogonalrank-one matrix pursuit method (OR1MP) in the sensethat multiple s candidates are identified per iteration bylow-rank matrix approximation. Owing to the selectionof multiple s candidates, our approach is finished withmuch smaller number of iterations when compared to theOR1MP. In addition, we extend the OR1MP algorithm todeal with tensor completion.

An-Bao XuHunan [email protected]

Dongxiu XieSchool of scienceBeijing Information Science and Technology [email protected]

Tin-Yau TamAuburn University

[email protected]

CP4

Sparse Approximation of Images by AdaptiveThinning

Anisotropic triangulations provide efficient methods forsparse image representations. We propose a locally adap-tive algorithm for sparse image approximation, adaptivethinning, which relies on linear splines on anisotropic tri-angulations. We discuss both theoretical and practical as-pects concerning image approximation by adaptive thin-ning. This includes asymptotically optimal N-term ap-proximations on relevant classes of target functions, suchas horizon functions across α Holder smooth boundariesand regular functions of Wα,p regularity, for α > 2/p− 1.

Armin IskeUniversity of HamburgDepartment of [email protected]

Laurent DemaretInstitute of Biomathematics and BiometryHelmholtz Zentrum Munchen, [email protected]

CP4

Joint Deconvolution and Blind Source Separationof Hyperspectral Data Using Sparsity

The hyperspectral restoration is very challenging when tak-ing into account not only the spectral mixing, but alsoblurring effects. We propose a new Blind Source Separa-tion method which addresses this problem by alternatingtwo minimizers, one solving a hyperspectral deconvolutionproblem using sparsity, and leading to a generalization ofthe FORWARD algorithm, and the second estimating themixing matrix by a least square inversion. A range of ex-amples illustrates the results.

Ming [email protected]

Jean-Luc Starck, Jerome BobinCEA [email protected], [email protected]

CP4

Sparse Source Reconstruction for NanomagneticRelaxometry

Source reconstruction for nanomagnetic relaxometry re-quires solving the magnetic inverse problem. By discretiz-ing the field of view, we can compute a lead field matrixthat relates the contribution of each pixel to the signal re-ceived by the detectors. We then approximate a minimuml0-norm solution by iterating over the minimization prob-lem:

minx

|| xi

wi||1 s.t. ||Ax− b||2 ≤ ε

Our approach for verification and validation of our algorith-mic implementation in phantom studies will be presented.

Sara Loupot, Wolfgang Stefan, Reza Medankan, KelseyMathieu, David Fuentes, John Hazle

70 IS16 Abstracts

University of Texas MD Anderson Cancer [email protected], [email protected],[email protected], [email protected],[email protected], [email protected]

CP4

Convolutional Laplacian Sparse Coding

We propose to extend the the standard convolutionalsparse representation by combining it with a non-localgraph Laplacian term. This additional term is chosen toaddress some of the deficiencies of the �1 norm in regular-izing these representations, and is shown to have an ad-vantage in both dictionary learning and an example imagereconstruction problem.

Xiyang LuoUniversity of California, Los [email protected]

Brendt WohlbergLos Alamos National LaboratoryTheoretical [email protected]

CP4

Gap Safe Rules for Speeding-Up Sparse Regular-ization

High dimensional regression / inverse problems might ben-efit from sparsity promoting regularizations. Screeningrules leverage the sparsity of the solution by ignoring somevariables in the optimization, hence speeding up solvers.When the procedure is proven not to discard featureswrongly, the rules are said to be ”safe”. We derive newsafe rules for generalized linear models regularized with L1or L1/L2 norms. The rules are based on duality gap com-putations allowing to safely discard more variables, in par-ticular for low regularization parameters. Our GAP Saferule can cope with any iterative solver and we illustrate itsperformance on Lasso, multi-task Lasso, binary and multi-nomial logistic regression, demonstrating significant speedups on all tested datasets with respect to previous saferules. This is a joint work with E. Ndiaye, O. Fercoq andA. Gramfort

Eugene NdiayeTelecom-ParisTech, CNRS LTCIUniversite [email protected]

Olivier FercoqTelecom-ParisTech, CNRS LTCIUniversite Paris-Saclay,75013, Paris, [email protected]

Alexandre GramfortTelecom-ParisTech, CNRS LTCIUniversite [email protected]

Joseph SalmonTelecom-ParisTech, CNRS [email protected]

CP5

Removal of Curtaining Effects by a Variational

Model with Directional Forward Differences

Focused ion beam tomography provides high resolution vol-umetric images on a micro scale. However, due to thephysical acquisition process the resulting images are oftencorrupted by a so-called curtaining effect. In this talk, anew convex variational model for removing such effects isproposed. More precisely, an infimal convolution model isapplied to split the corrupted 3D image into the clean im-age and two types of corruptions, namely a striped and alaminar part.

Jan Henrik FitschenUniversity of [email protected]

Jianwei MaDepartment of MathematicsHarbin Institute of [email protected]

Sebastian SchuffUniversity of [email protected]

CP5

NonLocal via Local–NonLinear via Linear: A NewPart-Coding Distance Field via Screened PoissonEquation

We propose a repeated use of Screened Poisson PDE tocompute a part coding field for perceptual tasks such asshape decomposition. Despite efficient local and linearcomputations, the field exhibits highly nonlinear and non-local behavior. Our scheme is applicable to shapes in ar-bitrary dimensions, even to those implied by fragmentedpartial contours. The local behavior is independent of theimage context in which the shape resides.

Murat Genctav, Asli Genctav, Sibel TariMiddle East Technical [email protected], [email protected],[email protected]

CP5

Boundary Formulation of Finite Differences: Anal-ysis and Applications

Estimation of numerical derivatives on the boundary valuesremains an unresolved dilemma in many inverse problems.Many formulations such as cyclic or Neumann conditionsviolate the derivative continuity and cause discrepancies.This presentation provides a numerical solution to calcu-late derivatives on the boundaries with high order polyno-mial accuracy in a unified convolution matrix. The numer-ical stability of this matrix is analyzed via the distributionof the eigenvalues and perturbation analysis and comparedto the existing formulations in the literature.

Mahdi S. Hosseini, Konstantinos N. PlataniotisUniversity of [email protected], [email protected]

CP5

Solving Variational Problems and Partial Differen-tial Equations That Map Between Manifolds Via

IS16 Abstracts 71

the Closest Point Method

Maps from a manifold M to a manifold N appear in im-age processing, medical imaging, and many other areas.This talk introduces a numerical framework for variationalproblems and PDEs that map between manifolds. Theproblem of solving a constrained PDE between M and Nis reduced into two simpler problems: solving a PDE onM and projecting onto N . Numerical examples of denois-ing texture maps, diffusing random maps, and enhancingcolour images are presented.

Nathan D. KingDepartment of MathematicsSimon Fraser [email protected]

Steven RuuthMathematicsSimon Fraser [email protected]

CP5

Regularization Strategy for Inverse Problem for1+1 Dimensional Wave Equation

An inverse boundary value problem for a 1+1 dimensionalwave equation with wave speed c(x) is considered. Wegive a regularisation strategy for inverting the map A :c �→ Λ, where Λ is the hyperbolic Neumann-to-Dirichletmap corresponding to the wave speed c. We consider thecase when we are given a perturbation of the Neumann-to-Dirichlet map Λ = Λ + E , and reconstruct an approximatewave speed c. Our regularization strategy is based on anew formula to compute c from Λ. Moreover we have donenumerical implementation and executed it with a simulateddata.

Jussi P. KorpelaUniversity of HelsinkiDepartment of Mathematics and [email protected]

CP5

Exploiting Sparsity in PDEs with DiscontinuousSolutions

Exploiting sparsity plays a central role in many recent de-velopments in imaging and other related fields. We use �1regularization techniques to promote sparsity in the edgesof PDEs with discontinuous solutions. This has led us tothe development of numerical algorithms that do not havethe restrictive stability conditions on time stepping thatnormally occur. With these methods we increase the ac-curacy of methods that do not account for sparsity in thesolution.

Theresa A. ScarnatiArizona State UniversitySchool of Mathematical & Statistical [email protected]

CP6

Extracting Plane Symmetry Group Informationfrom Tiles with Color Permutations

Repeating a base motif creates a tile with different symme-tries. A tile has color symmetry, if applying certain sym-

metry on a tile maps all regions of one color to the regionsof another color. In this work, we propose a novel ap-proach to extract the unit cells and fundamental domainsof tiles with various color symmetries, both considering andignoring color permutations. We use multiple ideas fromvariational and PDE based image processing methods.

Venera AdanovaMiddle East Technical [email protected]

Sibel TariComputer Engineering DepartmentMiddle East Technical University, [email protected]

CP6

New Techniques for Inversion of Full-Waveform In-duced Polarization Data

Induced polarization (IP) is a geophysical method thatmeasures electrical polarization of the subsurface. Stan-dard methods for inversion of IP data use simplified modelsthat neglect much of the information collected in modernsurveys, limiting imaging resolution. We are developinghigh performance multigrid based methods for modellingfull IP decay curves from large sources along with a cor-responding inversion algorithm that combines voxel-basedTikhonov regularized inversion with a parametric-level setapproach.

Patrick T. BelliveauUniversity of British [email protected]

Eldad HaberDepartment of MathematicsThe University of British [email protected]

CP6

Bidirectional Texture Function Bernoulli-MixtureCompound Texture Model

This paper introduces a method for modeling textures us-ing a parametric BTF compound Markov random fieldmodel. The purpose of our approach is to reproduce, com-press, and enlarge a given measured texture image so thatideally both natural and synthetic texture will be visuallyindiscernible. The model can also be applied to BTF mate-rial editing. The control field is generated by the Bernoullimixture model and the local textures are modeled usingthe 3DCAR.

Michal HaindlInstitute of Information Theory and Automation of [email protected]

CP6

Information Theoretic Approach for AcceleratedMagnetic Resonance Thermometry in the Presenceof Uncertainties

A model-based information theoretic approach is presentedto perform the task of Magnetic Resonance (MR) thermalimage reconstruction from a limited number of observedsamples on k-space. The key idea of the proposed approach

72 IS16 Abstracts

is to optimally detect samples of k-space that are infor-mation rich with respect to a model of the thermal dataacquisition. These highly informative k-space samples arethen used to refine the mathematical model and efficientlyreconstruct the image.

Reza Madankan, Wolfgang Stefan, ChristopherMacLellan, Samuel Fahrenholtz, Drew MitchellUniversity of Texas MD Anderson Cancer [email protected], [email protected],[email protected],[email protected],[email protected]

R.J. StaffordMD Anderson Cancer [email protected]

John HazleUniversity of Texas MD Anderson Cancer [email protected]

David FuenstesMD Anderson Cancer [email protected]

CP6

BLA: A Weak Form Attenuation CompensationModel for Ultrasonic Imagery

The quality of medical sonography is hindered by the shad-owing or enhancement artifacts due to acoustic wave prop-agation and attenuation across tissue layers. We presenta Backscatter-Levelset-Attenuation (BLA) joint estima-tion model in the context of regional ultrasound attenua-tion compensation and structural segmentation. The BLAmodel eliminates the need of solving PDEs over irregulardomains, and is formulated using level sets. We provide nu-merical algorithms along with discretization schemes. Themain advantage of the BLA method is its remarkable com-putational efficiency. We demonstrate the results usingsimulated, phantom and in vivo ultrasound images.

Jue WangUnion [email protected]

Yongjian YuUniversity of [email protected]

CP7

A Fractional Order Variational Model for OpticalFlow Estimation Based on Sparsity Algorithm

In this paper, a fractional order variational model is pro-posed for estimating the optical flow. The proposed frac-tional order model is introduced by generalizing an integerorder variational model formed with a global model of Hornand Schunck and the classical model of Nagel and Enkel-mann. In particular, the proposed model generalizes theexisting variational models from integer to fractional order,and therefore a more suitable in estimating the optical flow.However, it is difficult to solve this generalized model dueto the complex fractional order partial differential equa-tions. The Grunwald-Letnikov derivative is used to dis-cretize the fractional order derivative. The correspondingsparse linear system of equations is solved by using a spar-

sity algorithm in order to improve the convergence rate ofthe solution. The experimental results on different datasetsverify the validity of the proposed model.

Pushpendra KumarIndian Institute of Technology [email protected]

Sanjeev Kumar, Balasubramanian RamanIndian Institute of Technology [email protected], [email protected]

CP7

Optical Flow on Evolving Sphere-Like Surfaces

We consider optical flow on evolving surfaces which can beparametrised from the 2-sphere. Our main motivation is toestimate cell motion in time-lapse volumetric microscopyimages depicting fluorescently labelled cells of a live ze-brafish embryo. We exploit the fact that the recorded cellsfloat on the surface of the embryo and allow for the extrac-tion of an image sequence together with a sphere-like sur-face. We solve the resulting variational problem by meansof a Galerkin method based on vector spherical harmonicsand present numerical results.

Lukas F. LangRICAM, Austrian Academy of [email protected]

Otmar ScherzerComputational Science CenterUniversity [email protected]

CP7

Classification of Hyperspectral Data Using theBesov Norm

Sparse representations have been extensively studied inimage processing, however not much has been done withsparse-based classification problems. In this study, we dis-cuss the use of wavelets in hyperspectral imaging. Theanalysis-based approach accounts for more aspects of thedata than the coordinate-wise euclidean distance approach.We estimate the local properties of the hyperspectralstack using the Besov norm for a given choice of wavelet.Thereby, allowing for multiscale and multidirectional fea-tures.

Richard N. LarteyCase Western Reserve UniversityDepartment of Mathematics,Applied Mathematics [email protected]

Weihong GuoDepartment of Mathematics, Case Western [email protected]

Julia DobrosotskayaCase Western Reserve [email protected]

CP7

New Uncertainty Principles for Image Feature Ex-

IS16 Abstracts 73

traction

The motivation for this talk is window design for imagefeature extraction by a filter bank. There is a conven-tional framework for analyzing localization aspects of win-dow functions. We claim that the conventional frameworkis flawed, and develop a new adequate theory. Our ap-proach leads to new uncertainty principles and new optimalwindow functions. Filter banks based on our new optimalwindow functions have a certain notion of sparsity.

Ron LevieSchool of Mathematical Sciences,Tel Aviv University, Tel [email protected]

Nir SochenApplied Mathematics DepartmentTel Aviv [email protected]

CP7

Hyperspectral Video Analysis Using Graph Clus-tering Methods

Perhaps the most challenging imaging modality to analyzein terms of the vast size of the data are videos taken fromhyperspectral cameras. We consider an example involv-ing standoff detection of a gas plume involving Long WaveInfrared spectral data with 128 bands. Rather than usingPCA or a similar dimension reduction method we treat thisas a ”big data” classification problem and simultaneouslyprocess all pixels in the entire video using novel new graphclustering techniques. Computation of the entire similaritygraph is prohibitive for such data so we use the Nystromextension to randomly sample the graph and compute amodest number of eigenfunctions of the graph Laplacian.A very small part of the spectrum allows for spectral clus-tering of the data. However with a larger but still modestnumber of eigenfunctions we can solve a graph-cut basedsemi supervised or unsupervised machine learning problemto sort the pixels into classes. We discuss challenges ofrunning such code on both desktops and supercompers.

Gloria [email protected]

Ekaterina MerkurjevDepartment of [email protected]

Alice KonigesLawrence Berekely [email protected]

Andrea L. BertozziUCLA Department of [email protected]

CP7

Image Segmentation with a Shape Prior

We study variational models for segmentation incorporat-ing a shape prior, and our method involves computing theglobal minimiser of a functional with fixed fitting terms.We define this prior implicitly in such a way that the imageintensity information is incorporated into the minimisation

of the affine parameters of the registration step, improvingthe model’s reliability. We discuss how this approach com-pares to similar methods, and present numerical results todemonstrate its performance.

Jack A. Spencer, Ke ChenUniversity of [email protected], [email protected]

CP8

Error Estimates and Convergence Rates for Fil-tered Back Projection

The filtered back projection (FBP) formula allows us toreconstruct bivariate functions from given Radon samples.However, the FBP formula is numerically unstable and low-pass filters of finite bandwidth are employed to make the re-construction less sensitive to noise. In this talk we analysethe intrinsic reconstruction error incurred by the low-passfilter. We prove L2-error estimates on Sobolev spaces offractional order along with asymptotic convergence rates,where the bandwidth goes to infinity.

Matthias BeckmannUniversity of [email protected]

Armin IskeUniversity of HamburgDepartment of [email protected]

CP8

Density Compensation Factor Design for Non-Uniform Fast Fourier Transforms

In applications such as magnetic resonance imaging (MRI),radar imaging, and radio astronomy, data may be col-lected as a sequence of non-uniform Fourier samples. Onecommon approach used to reconstruct images from non-uniform Fourier data involves regridding the non-uniformFourier data to uniform points, and then applying theFFT, a process often referred to as the non-uniformFFT (NFFT). In the regridding process, parameters oftentermed the density compensation factors (DCFs) are usedessentially as quadrature weights to construct the inverseFourier transform. The DCFs are typically chosen usingheuristic arguments, and, depending on the sampling pat-tern, may not lead to a convergent approximation. In thistalk we illustrate the importance of choosing DCFs appro-priately. We develop an algorithm to design DCFs basedon the given sampling scheme and demonstrate numericalconvergence. We further apply our algorithm to recoverfeatures (such as edges) of the underlying image, which isespecially useful in target identification or tissue classifica-tion.

Anne GelbArizona State [email protected]

CP8

The Factorization Method for Imaging Defects inAnisotropic Materials

In this presentation we consider the inverse acoustic orelectromagnetic scattering problem of reconstructing pos-sibly multiple defective penetrable regions in a known

74 IS16 Abstracts

anisotropic material of compact support. We develop thefactorization method for a non-absorbing anisotropic back-ground media containing penetrable defects. In particular,under appropriate assumptions on the anisotropic materialproperties of the media we develop a rigorous characteriza-tion for the support of the defective regions form the givenfair field measurements. Finally we present some numeri-cal examples in the two dimensional case to demonstratethe feasibility of our reconstruction method including ex-amples for the case when the defects are voids (i.e. sub-regions with refractive index the same as the backgroundoutside the inhomogeneous hosting media).

Isaac HarrisTexas A&M UniversityDepartment of [email protected]

Fioralba CakoniRutgers UniversityDepartment of [email protected]

CP8

Ghosting in Principal Component Pursuit: An In-cremental Approach

In video background modeling, ghosting occurs when anobject that belongs to the background is detected in theforeground. In the context of PCP, this usually occurswhen a moving object occludes a highly distinguishablebackground’s object. Based on a previously developed in-cremental PCP method, we propose a method to identifyand eliminate the ghosting effect. It is based on incremen-tal rank-1 SVD updates and on the analysis of the currentbackground estimate.

Paul RodriguezPontifical Catholic University of [email protected]

Brendt WohlbergLos Alamos National [email protected]

CP8

Stochastic Image Interpolation with Positional Er-rors

We consider the interpolation of sparsely sampled imageinformation when the location of the collecting sensor isuncertain. A Gaussian Process model is employed jointlydetermining the image data and the sensor locations undervarious statistical models for the stochastic locations. An-alytical tools are developed for quantifying the maximalvariance in location uncertainly that can be tolerated toensure a level of interpolation fidelity. Application to theinterpolation of CubeSat radiometer data is considered.

Weitong RuanTufts UniversityDepartment of Electrical and Computer [email protected]

Adam Milstein, William BlackwellMIT Lincoln LabSensor Technology and System [email protected], [email protected]

Eric MillerTufts [email protected]

CP8

Nonlinear Parametric Inversion Using Randomiza-tion

In PDE-based inverse problems with many measurements,we have to solve many large-scale discretized PDEs for eachevaluation of the misfit or objective function. In the nonlin-ear case, each time the Jacobian is evaluated an additionalset of systems must be solved. This leads to a tremendouscomputational cost. Our approach leads to solutions of thesame quality as obtained using all sources and detectorsbut at a greatly reduced computational cost.

Selin SariaydinDepartment of MathematicsVirginia [email protected]

Eric De SturlerVirginia [email protected]

Misha E. KilmerMathematics DepartmentTufts [email protected]

CP9

Linear Inverse Mri Approximation from NonlinearMri

Magnetic resonance imaging (MRI) produces a complex-valued multivoxel image. Its magnitude is nonlinearly re-lated to the magnetic susceptibility (χ) source; whereasits phase is linearly related to the χ source in the smallphase angle regime, which enables χ reconstruction by solv-ing a linear inverse MRI problem. The involved ill-poseddipole inversion is solved by a total-variation-regularizedsplit Bregman (TVB) algorithm. In large phase angle sce-narios, the inverse MRI solution becomes nonlinear.

Zikuan Z. ChenThe Mind Research [email protected]

Vince CalhounThe University of New [email protected]

CP9

The Partial Volume Problem in Magnetic Reso-nance Fingerprinting from a Bayesian Perspective

Magnetic resonance fingerprinting (Ma et al, Nature 2013)produces quantitative maps of parameters such as T1 andT2 relaxation times. However, pixels containing signalfrom multiple tissue types may be incorrectly mapped. Themixed signal is y = Ax + ξ where A is a dictionary con-taining simulated signal evolutions and x determines thecontribution of each entry. We solve the system in theBayesian framework, using the prior density to encouragesparsity of x.

Debra F. McGivney

IS16 Abstracts 75

[email protected]

Anagha Deshmane, Yun JiangDepartment of Biomedical EngineeringCase Western Reserve [email protected], [email protected]

Dan Ma, Mark GriswoldDepartment of RadiologyCase Western Reserve [email protected], [email protected]

CP9

MIND Demons: Symmetric Diffeomorphic De-formable Registration of MR and CT Images

A symmetric diffeomorphic 3D image registration al-gorithm –“MIND Demons’– was developed to estimatenonrigid image transformations incorporating modality-independent-neighborhood descriptors (MIND) and a Hu-ber metric for non-linear MR-CT image intensity non-correspondence. The algorithm optimizes viscoelastic dif-feomorphisms under geodesic, smoothness, and invert-ibility constraints by alternating fast Gauss-Newton op-timization and Tikhonov regularization in a multireso-lution scheme. Applications to spine surgery demon-strated improved registration accuracy (1-2 mm) and sub-voxel inverse-consistency (0.008 mm) compared to mutual-information-based Demons and B-spline methods.

Sureerat Reaungamornrat, Tharindu De Silva, Ali UneriJohns Hopkins [email protected], [email protected], [email protected]

Sebastian Vogt, Gerhard KleinszSiemens Healthcare XPErlangen, [email protected],[email protected]

Akhil KhannaJohns Hopkins Orthopaedic [email protected]

Jean-Paul WolinskyJohns Hopkins [email protected]

Jerry L. PrinceJohns Hopkins UniversityElectrical and Computer [email protected]

Jeffrey SiewerdsenJohns Hopkins [email protected]

CP9

Background Signal Suppression for Magnet Reso-nance (mr) Phase Images

MR images have a magnitude and a phase, but in almost allclinical applications only the magnitude images are used,because the phase images have a smooth but strong back-ground signal that masks useful information. The phasecontains information such as the temperature during ther-mal ablation, and the iron content of brain tissue. We

present a novel method to suppress the background thatis based on higher order edge detection and sparse imagerepresentation.

Wolfgang Stefan, David FuentesUniversity of Texas MD Anderson Cancer [email protected], [email protected]

Erol [email protected]

Ken-Pin Hwang, John D. Hazle, R. Jason StaffordThe University of Texas MD [email protected], [email protected],jstafford

CP9

Non-Linear Optical Flow for Lung Ct Registration

The registration of lung CT images plays an importantrole in effective treatment planning and tracking of medi-cal conditions effecting the lungs, for example tumours, assuch fast and accurate registration algorithms are required.In this talk I will describe and compare several non-linearoptical flow methods in order to ascertain how well theyregister sets of lung CT data. I will also discuss results ofnew models and solution approaches from combining seg-mentation and registration.

Anthony M. Thompson, Ke ChenUniversity of [email protected], [email protected]

Colin Baker, John FenwickClatterbridge Cancer [email protected],[email protected]

CP10

Non-Stationary Blind Super-Resolution

Super-resolution is generally referred to as the task of iden-tifying unknown parameters from coarse information. Mo-tivated by applications such as single molecule imaging,radar imaging, etc, we consider the problem of parame-ter estimation of complex exponentials from their modula-tions with unknown waveforms, allowing for non-stationaryblind super-resolution. This problem, however, is ex-tremely ill-posed since both the parameters associated withthe complex exponentials and modulating waveforms areunknown. To alleviate this, we assume that the unknownwaveforms live in a common low-dimensional random sub-space. Using a lifting trick, we recast this bilinear inverseproblem as a parametrized low-rank matrix recovery prob-lem from random sensing measurements. An atomic normminimization problem is then formulated, which is equiv-alent to a computationally efficient semidefinite program.We show that, up to the scaling ambiguities, exact recoveryof both of the parameters of complex exponentials and thesamples of the unknown waveforms is possible when thenumber of measurements is proportional to the number ofdegrees of freedom in the problem. Numerical simulationsare conducted to support our theoretical findings, whichshow that non-stationary blind super-resolution using con-vex programming is possible.

Gongguo Tang, Dehui YangColorado School of Mines

76 IS16 Abstracts

[email protected], [email protected]

Michael B. WakinDept. of Electrical Engineering and Computer ScienceColorado School of [email protected]

CP10

A Vectorial Total Generalized Variational Modelfor Multichannel Sar Image Speckle Suppression

It is a challenging task for multichannel SAR image specklesuppression, especially for those with important details andfeatures. We proposed a novel vectorial total variationalmodel which integrates total generalized variation. Thisnovel model regularizes different image regions at differ-ent levels and suppresses speckle with better edges andfine details than the existing regularization models. Somenumerical simulations are presented to show that the reg-ularizer preserves various image features much better thanthe VTV.

Tan XintongCollege of Science, National University of DefenseTechnologxintong [email protected]

Yu Qi, Wang ZelongCollege of ScienceNational University of Defense [email protected], zelong [email protected]

Liu JiyingJiying [email protected] University of Defense [email protected]

Zhu JuboCollege of ScienceNational University of Defense Technologyju bo [email protected]

CP10

A Locally Adaptive Wiener Filter in Graph FourierDomain for Improved Image Denoising

We propose a Wiener filtering scheme in graph Fourier do-main for improving image denoising performance achievedby spectral graph based denoising methods. It employsgraph Fourier coefficients of the noisy image that are al-ready processed for denoising, to estimate a Wiener filterthat further improves the achieved denoising performance;and can be applied patchwise adaptively, or to the entireimage. We report higher peak signal-to-noise ratio figuresthan BM3D method for some images.

M. Tankut OzgenAnadolu UniversityAnadolu [email protected]

Ali Can YaganDept. Electrical and Electronics Eng., Anadolu UniversityFaculty of Engineering, Anadolu Univ., Eskisehir, Turkey

[email protected]

CP10

On Diffeomorfic Image Registration Models andTheir Effective Solution Algorithms

Image registration is a process of finding correspondencesbetween two different dates. But in large deformationregistration problems, it is very difficult to obtain a so-lution with no folding. J.Modersitzki (2004,2007) andL.M.Lui(2014) have used Jacobian determinant and Bel-trami coefficient to avoid the twist. We propose a novelmodel combining Jacobian determinant and Beltrami co-efficient to get a diffeomorfic transformation. Numericalresults demonstrate that our model can have a good effecton the large deformation.

Daoping ZhangDepartment of Mathematical ScienceThe University of [email protected]

Ke ChenUniversity of [email protected]

CP10

CITRUS: Cueing Image Target Regions by Unmix-ing Spectra

Target detection in remotely sensed hyperspectral imagerytraditionally seeks the specific pixels that contain a givenmaterial of interest. In this study, we give up some preci-sion in spatial target location in exchange for a lower falsealarm rate. Instead of pixels, we seek regions (or tiles) thatcontain target material. The detection map highlights thetiles with high per-tile detection scores, and serves as avisual cueing tool for an analyst.

Amanda K. ZiemannLos Alamos National [email protected]

James TheilerSpace and Remote Sensing SciencesLos Alamos National [email protected]

CP11

A Max-Cut Approach to the Heterogeneity Prob-lem in Cryo-Electron Microscopy

The problem in single particle reconstruction is to estimatethe structure of a molecule given a set of projection im-ages. When the set contains images of two or more typesof molecules, one needs to classify the images. In manycases this problem is unsolved. We present an algorithmfor reconstruction of all the structures in a heterogeneousproblem. We prove theoretical bounds on the performanceof the algorithm, and show results on real data.

Yariv AizenbudDepartment of Applied Mathematics, School ofMathematicalSciences, Tel Aviv [email protected]

Yoel Shkolnisky

IS16 Abstracts 77

Tel Aviv [email protected]

CP11

Single Particle Tracking of Blinking Particles

Live cell imaging experiments frequently generate largevolumes of time-lapse image data. The desired infor-mation often corresponds to the trajectories of individ-ual, fluorescently-labeled particles, making single particletracking (SPT) a critical component of the image anal-ysis pipeline. Complicating the analysis, often the fluo-rescent labels employed either blink or can only be de-tected intermittently due to their low signal-to-noise. Ann-dimensional, graph theory based SPT algorithm has beendeveloped, explicitly designed for tracking intermittent ob-servations.

Stephen M. AnthonySandia National [email protected]

Kejia ChenUniversity of [email protected]

Steve GranickUlsan National Institute of Science and [email protected]

CP11

Multiscale Imaging of Carbonate Rocks and 3DStochastic Reconstruction for Digital Rock Physics

Nano-porous geomaterials are important for subsurfaceemerging problems. We apply integrated multiscale imag-ing of carbonate rock from nanometer to centimeter scalesto characterize 3D structures and mineral distributions forpetrophysical and mechanical properties from the nanome-ter to centimeter scales. With primary pore textures hon-ored, 3D digital pore networks can be reconstructed usingseveral stochastic approaches. Lattice Boltzmann methodis used to obtain tortuosity and permeability at severaldifferent scales.

Hongkyu YoonGeoscience Research and ApplicationsSandia National [email protected]

Jonghyun LeeStanford [email protected]

Thomas DewersGeoscience Research and ApplicationsSandia National [email protected]

CP11

The Role of Visual Saliency in Seismic Interpreta-tion with An Application to Salt Dome Delineation

We propose a new saliency-based seismic attribute forcomputer-assisted interpretation of large seismic volumes.We further propose a framework to delineate salt domestructures using saliency and visual attention theory. Theexperimental results on the real seismic dataset acquired

from the North Sea, F3 block show the effectiveness of theproposed framework using both subjective and objectiveevaluation measures. The proposed framework has a verypromising future in effective seismic interpretation. In thiswork, we demonstrate that viewing the large seismic vol-umes as a scene with underlying hypotheses and structuresis a very promising direction.

Muhammad Amir ShafiqGeorgia Institute of TechnologyAtlanta, Georgia, [email protected]

Tariq Alshawi, Zhiling Long, Ghassan AlRegibGeorgia Institute of Technology,Atlanta, Georgia, [email protected], [email protected], [email protected]

CP11

Stochastic Methods on Geophysical Inverse Prob-lems

Stochastic optimization methods, like stochastic gradientdescent and stochastic average gradient, show fast initialconvergence on the first iteration rounds and use only asubset of the data at a time. We study the use of thesemethods when solving computationally demanding geo-physical inverse problems. These problems are ill-posed,with unknown noise and large data sets. Our goal is to usethe stochastic aspect to find an appropriate halting timeto avoid over-fitting the data.

Sanna K. Tyrvainen, Eldad HaberUniversity of British [email protected], [email protected]

MS1

Second Order TV-Type Regularization Methodsfor Manifold-Valued Images

In many real world situations, measured data is noisy andnonlinear, i.e., the data is given as values in a certainmanifold. Examples are Interferometric Synthetic Aper-ture Radar (InSAR) images or the hue channel of HSV,where the entries are phase-valued, directions in R

n, whichare data given on S

n−1, and diffusion tensor magnetic reso-nance imaging (DT-MRI), where the obtained pixel of theimage are symmetric positive definite matrices. In this talkwe extend the recently introduced total variation model onmanifolds by a second order TV type model. We first in-troduce second order differences on manifolds in a soundway using the induced metric on Riemannian manifolds.By avoiding a definition involving tangent bundles, thisdefinition allows for a minimization employing the inexactcyclic proximal point algorithm, where the proximal mapscan be computed using Jacobian fields. The algorithm isthen applied to several examples on the aforementionedmanifolds to illustrate the efficiency of the algorithm. Thisis joint work with M. Back, J. Persch, G. Steidl, and A.Weinmann.

Ronny BergmannUniversity of [email protected]

MS1

A Primal-Dual Extragradient Method for Nonlin-

78 IS16 Abstracts

ear Forward Models in Function Spaces

Abstract not available.

Christian ClasonUniversity of Duisburg-EssenFaculty of [email protected]

MS1

Variable Metric Line-Search Methods for Non-smooth Convex and Non-Convex Optimization,with Applications in Imaging

Iterative algorithms for the numerical solution of non-smooth optimization problems involving an objective func-tion that is a combination of a data misfit term and reg-ularizing penalty are discussed. The proposed algorithmsare based on variable metrics, descent directions and theArmijo line-search rule. Convergence results are given inthe convex and non-convex case, and are also examined incase the proximal operator of the non-smooth part of theobjective function can only be calculated approximately.Based on joint work with S. Bonettini, F. Porta, M. Pratoand S. Rebegoldi.

Ignace Loris

FNRS Chercheur Qualifie (ULB, Brussels)[email protected]

MS1

Coordinate Update Methods in Image Processingand Machine Learning

This talk focuses on a class of algorithms, called coordi-nate update algorithms, which are useful at solving large-sized problems involving linear and nonlinear mappings,and smooth and nonsmooth functions. They decomposea problem to simple subproblems, where each subprob-lem updates one, or a small block of, variables each time.The coordinate update method sits a high-level of ab-straction and include many special cases such as Jacobi,Gauss Seidel, and coordinate descent methods. They havefound applications throughout signal/imaging processing,differential equations, and machine learning. We abstractmany problems to the fixed-point problem x = Tx. Thistalk discusses the favorable structures of the operator Tthat enable highly efficient coordinate update iteration:xk+1i = (Txk)i. It can be carried out in sequential, paral-

lel, or async-parallel fashions. We introduce new scalablecoordinate-update algorithms to many problems involvingcoupling constraints Ax = b, composite nonsmooth func-tions f(Ax), and large-scale data. We present numericalexamples with hundreds of gigabytes of data.

Zhimin PengUniversity of California. Los AngelesDepartment of [email protected]

Tianyu WuUniversity of California, Los [email protected]

Yangyang XuInstitute for Mathematics and its [email protected]

Ming YanMichigan State UniversityDepartment of [email protected]

Wotao YinUniversity of California at Los [email protected]

MS2

Convex Relaxation Methods for Computer Vision

Numerous problems in computer vision and image analysiscan be solved by optimization methods. Yet, many clas-sical approaches correspond to non-convex energies whichleads to suboptimal solutions and often strong dependencyon appropriate initialization. In my presentation, I willshow how problems like stereo or multiple view reconstruc-tion, segmentation and 3D shape matching can be tackledby means of convex relaxation methods which allow to effi-ciently compute globally optimal or near-optimal solutions.The arising large-scale convex problems can be solved bymeans of efficient and provably convergent primal-dual al-gorithms. They are easily parallelized on GPUs providinghigh-quality solutions in acceptable runtimes.

Daniel CremersTechnical University of Munich (TUM)[email protected]

MS2

Partial Optimality in Discrete Problems Based onTheir Polyhedral Relaxations

We propose a sufficient condition for optimality of a partof a relaxed solution to the original discrete optimizationproblem. It generalizes previous results on persistency invertex packing, pseudo-Boolean optimization, 0-1 polyno-mial programming as well as a number of methods for par-tial optimality in multilabel energy minimization (generalgraphical models). We show that the maximum subsetof variables satisfying the condition can be determined inpolynomial time and propose an efficient implementationfor pairwise models.

Alexander ShekhovtsovInstitute for Computer Graphics and Vision (ICG) GrazUniverInffeldgasse 16, Graz 8010, [email protected]

Paul SwobodaImage and Pattern Analysis GroupHeidelberg University, [email protected]

Bogdan SavchynskyyComputer Vision Lab, Institute for Artificial IntelligenceDresden University of [email protected]

MS2

A Semidefinite Relaxation for Computing Dis-tances Between Metric Spaces

In this talk we explore a semidefinite relaxation for a met-ric between point clouds. We derive an algorithm basedon alternating direction augmented Lagrangian that can

IS16 Abstracts 79

efficiently compute the distance between point clouds withhundreds of points.

Rachel WardDepartment of MathematicsUniversity of Texas at [email protected]

Soledad VillarUniversity of Texas at [email protected]

MS2

(Discrete-Continuous Optimization)2 for Com-puter Vision

In this talk we discuss two convex relaxations for imageprocessing that contain discrete and continuous aspects.The first relaxation addresses discrete labeling problems(i.e. multi-class segmentation) on continuous domains andtheir relation to local polytope relaxations well known inmachine learning. The second convex relaxation addressescontinuous labeling problems on discrete graph structures,which allows to model jointly combinatorial and continuousproblems.

Christopher ZachToshiba Research Europe Ltd., Cambridge ResearchLaboratory208 Cambridge Science Park, Milton Road, Cambridge,CB4 [email protected]

MS3

Recent Advances in Transform Learning for BlindCompressed Sensing in Imaging

Sparse signal modeling using synthesis or analysis dictio-nary learning involves approximations of NP-hard sparsecoding, and expensive learning steps. Recently, sparsifyingtransform learning (STL) received interest for its cheap andexact closed-form solutions to iteration steps. We presentseveral extensions to this framework: (i) online STL, forbig data and video denoising; (ii) a union of transformsmodel with greater representation power; and (iii) filterbank STL acting on entire images rather than on patches.

Yoram BreslerDepartment of Electrical and Computer Engineering andtheCoordinated Science Laboratory, University of [email protected]

MS3

Flexible Multi-layer Sparse Approximations of Ma-trices and Applications

Non-adaptive analytic dictionaries such as the Fourier orwavelet matrices benefit from fast algorithms. On theother hand, adaptive learned dictionaries traditionally suf-fer from their high computational complexity. We proposea dictionary structure that is both adaptive and computa-tionally efficient. We investigate the applicability of thisdictionary structure to both reconstructive and predictivedictionary learning, and explore its generalization proper-ties.

Luc Le MagoarouInria Rennes

Bretagne [email protected]

Remi GribonvalINRIA Rennes - Bretagne [email protected]

MS3

On Fast Transform Optimization

We study a strategy to optimize sparse convolution ker-nels leaving on the edges of a tree. They define a fasttransform and target atoms prescribed by the user. Theso-constructed (deep) optimization problem is smooth butmight be strongly non-convex. Experiments shows thatfast transforms can be optimized and opens many perspec-tives.

Francois MalgouyresInstitut de Mathematiques de ToulouseUniversite Paul [email protected]

Olivier Chabiron, Jean-Yves Tourn Tourneret, [email protected], [email protected], [email protected]

MS3

Trainlets: Dictionary Learning in High-Dimension

Dictionary Learning has traditionally been restricted tosmall dimensions due to computational constraints. Wepresent a method based on a new cropped wavelets de-composition, enabling a multi-scale decomposition withoutconsiderable border effects, and employ it within a doublesparsity model. We propose an online sparse dictionarylearning algorithm to train this model effectively, enablingit to handle very large training sets and big dimensions,obtaining large adaptable atoms that we call trainlets.

Jeremias SulamComputer Science Deparment, [email protected]

Michael EladComputer Science [email protected]

MS4

Markov Chain Monte Carlo Methods for InverseProblems Involving Partial Differential Equations

The application of MCMC methods to large-scale inverseproblems presents many interesting challenges and researchquestions. In this talk, I will present two Markov chainMonte Carlo (MCMC) methods for inverse problems. Iwill first consider cases in which the forward model is lin-ear and the regularization operator is defined by a partialdifferential equation, yielding a Gaussian Markov randomfield prior and a Gibbs sampler for sampling both the un-known parameters and the scaling parameters for the noiseand prior. I will then move on to the case in which the for-ward model is defined by a partial differential equation,yielding a nonlinear inverse problem, and a Metropolis-Hasting method with a proposal defined via an application

80 IS16 Abstracts

of an optimization method.

Johnathan M. BardsleyUniversity of [email protected]

MS4

A Large-Scale Ensemble Transform Method forBayesian Inverse Problems Governed by PDEs

We present an ensemble-based method for transformingprior samples to posterior ones. This method avoidsMarkov chain simulation and hence discarding expensivework when a sample is rejected. The idea is to cast theproblem of finding posterior samples into a large-scale lin-ear programming problems for which efficient and scalablesolver can be developed. Large-scale numerical results willbe presented to demonstrate the capability of the method.Authors: Aaron Myers, Alexandre Thiery, Kainan Wang,and Tan Bui-Thanh

Tan Bui-ThanhThe University of Texas at [email protected]

MS4

Statistical Inversion In Electrical Impedance To-mography For Damage Detection In Concrete

In this presentation, we will present the formulation ofthe statistical inversion for damage detection in civil engi-neering structures using Electrical Impedance Tomography(EIT). We will present a recently proposed Pilot AdaptiveMetropolis algorithm for image reconstruction. We willdiscuss our preliminary results using experimental data.

Thilo StraussUniversity of [email protected]

Taufiquar R. KhanClemson [email protected]

MS5

Iterative Joint Regularization in Multichannel Im-age Reconstruction via Bregman Distances

Motivated by the idea to exploit the often encounteredsimilarity of structures in different image channels we gen-eralize and extend the concept of Bregman iterations [S.Osher et al., An iterative regularization method for to-tal variation-based image restoration, SIAM MultiscaleModel. Simul., 4 (2005), pp. 460-489] to multichanneldata: For one-homogeneous functionals a joint subgradientis iteratively enforced by the use of Bregman distances be-tween different channels. Focussing on TV regularization,we give a geometric interpretation of the Bregman distanceand present some results on RGB-images illustrating howsolutions with joint edge sets are promoted.

Eva-Maria BrinkmannWWU [email protected]

Martin BurgerUniversity of MuensterMuenster, Germany

[email protected]

Michael MoellerDepartment of Computer ScienceTechnical University of Munich (TUM), [email protected]

Julian RaschInstitute for Computational and Applied Mathematics,WWU [email protected]

Tamara SeyboldResearch and Development, Arnold and RichterCinetechnikD - 80799 Munchen, [email protected]

MS5

Joint Mr-Pet Reconstruction Using Nuclear NormBased Multi-Channel Tgv Regularization

We propose a joint MR-PET reconstruction approach thatregards the two modalities as different channels of a singleimage and employs multi-channel total generalized varia-tion regularization. The gradients of the two channels arecoupled via a point-wise nuclear norm. This promotes spar-sity of the singular values of the joint Jacobian and hencealigns edges independent of the image constrast. In-vivoexperiments show a substantially improved reconstructionquality compared to both standard methods and separateregularization.

Martin HollerUniversity of [email protected]

Florian Knoll, Thomas Koesters, Ricardo OtazoNew York University School of [email protected], [email protected],[email protected]

Kristian BrediesUniversity of GrazInstitute of Mathematics and Scientific [email protected]

Daniel K SodicksonNew York University School of [email protected]

MS5

Structural Regularization for fMRI

We present construction of a structural regularization forfMRI with sparsely sampled data. The anatomical priorinformation for the construction of the regularization func-tional is extracted from a densely sampled MRI framewhich is acquired as part of the fMRI measurement proto-col. The approach is evaluated using simulated measure-ment data and experimental data taken from a Wistar ratspecimen using a 9.4T small animal MRI scanner.

Ville P. KolehmainenDepartment of Applied PhysicsUniversity of Eastern Finland

IS16 Abstracts 81

[email protected]

MS5

Molecular Particle Imaging: Basic Models, Math-ematical Challenges and First Results

We will present the basic mathematical model of MPI andits related challenges. Our goal is to combine MPI withmagnetic resonance imaging, which however, requires toregister images displaying different physical quantities. i.e.the different reconstructions do not share dominant land-mark structures besides the general morphological informa-tion contained in the region of interest of the MPI sources.We will outline our proposed approach for MPI-MR bi-modal imaging.

Peter MaassCenter for Industrial MathematicsUniversity of [email protected]

Christine BathkeUniversity of [email protected]

MS6

Curvature based Seeded Watershed for ClumpedObject Segmentation

Segmentation of 3D images containing clumped objects ofdifferent characteristics is very important in many appli-cations such as cell counting in biology, but can be quitechallenging. In such applications, the watershed transformis efficient given reasonable set of markers, but otherwiseleads to over-segmentation in the presence of low-contrastvariation or excessive noise. Interpreting a 3D image as3-manifold in 4D space, this talk will focus on seeded wa-tershed using geometric properties of hypersurfaces.

Thomas Atta-FosuCase Western Reserve [email protected]


MS6

Multiphase Image Segmentation Via Equally Dis-tanced Multiple Well Potential

We propose a family of functionals defined on vector valuedfunctions that involve a multiple well potential of the typearising in diffuse-interface models of phase transitions. Apotential with equally distanced wells makes it possible toretrieve the penalization of the true (i.e., not weighted)length of the boundaries.

Sung Ha KangGeorgia Inst. of [email protected]

Riccardo MarchIstituto per le Applicazioni del Calcolo, CNR

[email protected]

MS6

A Wavelet Frame Method with Shape Prior for Ul-trasound Video Segmentation

Ultrasound video segmentation is a challenging task due tolow contrast, shadow effects, complex noise statistics, andthe needs of high precision and efficiency for real time appli-cations such as operation navigation and therapy planning.In this paper, we propose a wavelet frame based video seg-mentation framework incorporating different noise statis-tics and sequential distance shape priors. The proposedindividual frame nonconvex segmentation model is solvedby a proximal alternating minimization algorithm and theconvergence of the scheme is established based on the re-cently proposed Kurdyka- Lojasiewicz property. The per-formance of the overall method is demonstrated throughnumerical results on two real ultrasound video data sets.The proposed method is shown to achieve better resultscompared to related level sets models and edge indicatorshape priors, in terms of both segmentation quality andcomputational time

Jiulong Liu, Xiaoqun ZhangShanghai Jiao Tong [email protected], [email protected]

Bin DongPeking [email protected]

Zuowei ShenNational University of [email protected]

MS6

Image Segmentation with Dynamic Artifacts De-tection and Bias Correction

The Chan-Vese (CV) model for region-based image seg-mentation fails when images are affected by artifacts (out-liers) and illumination bias. Here, we introduce a modelfor segmenting such images. In a single energy functional,we introduce a dynamic artifact class preventing intensityoutliers from skewing the segmentation, and in Retinex-fashion, we decompose the image into a piecewise-constantstructural part and a smooth bias part. The segmentationonly acts on the structure, only in regions not identified asartifacts, and is efficiently optimized using threshold dy-namics.

Dominique ZossoUniversity of California, Los AngelesDepartment of [email protected]


MS7

Efficient Hybrid Iterative Methods for Bayesian In-verse Problems

Inverse problems arise in various scientific applications, andBayesian approaches are often used for solving statisticalinverse problems, where unknowns are modeled as random

82 IS16 Abstracts

fields and Bayes rule is used to infer unknown parametersby conditioning on measurements. In this work, we de-velop hybrid iterative methods for computing maximum aposteriori estimators, for problems where the prior covari-ance matrix is accessed directly. Our approach is differentfrom previous approaches since we avoid forming (eitherexplicitly, or matvecs with) the square root or inverse ofthe prior covariance matrix. Instead, we make an appro-priate change of variables and consider a hybrid Golub-Kahan bidiagonalization iterative process with weightedinner products. The proposed algorithm is efficient andscalable to large problem sizes and has the benefit that reg-ularization parameters can be determined automatically.

Julianne ChungDepartment of MathematicsVirginia [email protected]

Arvind SaibabaNorth Carolina State [email protected]

MS7

Truncation Methods for Hybrid Regularization

Hybrid regularization methods allow efficient regulariza-tion of inverse problems after projection on a subspace.However, if convergence is slow, the memory requirementsmay be a problem. Hence we consider truncation tech-niques for hybrid methods.

Eric De Sturler, Julianne ChungVirginia [email protected], [email protected]

Geoffrey DillonVirginia Tech [email protected]

MS7

An Incremental Proximal Gradient Method forSpectral Computerized Tomography

In contrast to conventional computerized tomography(CT), spectral CT accounts for the polyenergetic nature ofx-rays. Improved modeling can not only reduce artifactsbut also provide additional information. However, the aris-ing inverse problem is nonlinear and standard reconstruc-tion techniques are not directly applicable. This presen-tation discusses a computationally efficient algorithm forspectral CT based on incremental proximal gradient meth-ods. Joint work with Martin S. Andersen and Jakob S.Jorgensen, Technical University of Denmark.

Lauri HarhanenDTU [email protected]

Martin S. AndersenUniversity of California, Los AngelesElectrical Engineering [email protected]

Jakob JorgensenTechnical University of Denmark

[email protected]

MS7

Robust Regression for Mixed Poisson GaussianModel

We consider image deblurring problem with Poisson dataand additive Gaussian noise. The maximum likelihoodfunctional for this model can be approximated by aweighted least squares problem with the weights dependingon the computed data. However, the least squares solutionis not robust if outliers occur. We propose a modification ofthe data fidelity function using the idea of robust regres-sion and test the resulting method on data with varioustypes of outliers.

Marie KubinovaAcademy of Sciences of the Czech [email protected]

James G. NagyEmory UniversityDepartment of Math and Computer [email protected]

MS8

A Convex Variational Approach for RestoringBlurred Images with Cauchy Noise

Over the years, many variational models have been intro-duced for removing Gaussian noise, Poisson noise, multi-plicative noise, and impulse noise. In this talk, we focuson a very impulsive noise, the so-called Cauchy noise. In-spired by the ROF model, we propose a convex variationalmodel, based on total variation as the regularization term,for restoring images with blur and Cauchy noise. Numeri-cal experiments show that our approach outperforms otherwell-known methods.

Federica SciacchitanoTechnical University of DenmarkDepartment of Applied Mathematics and [email protected]

MS8

A Majorization-Minimization Generalized KrylovSubspace Methods for Lp-Lq Image Restoration

A new majorization-minimization framework for lp-lq im-age restoration is presented. The solutions are soughtin generalized Krylov subspaces that are build up duringthe solution process. Computed examples illustrate thathigh-quality restorations can be determined with a mod-est number of iterations and that the storage requirementof the method is not very large. A comparison with re-lated methods shows the competitiveness of the methodproposed. Numerical examples with different p and q showthe promising results for non-Gaussian noises.

Fiorella SgallariUniversity of BolognaDepartment of [email protected]

Alessandro LanzaDept.Mathematics, Univ. Bologna, [email protected]

IS16 Abstracts 83

Serena MorigiDepartment of MathematicsUniversity of Bologna, [email protected]

Lothar ReichelKent State [email protected]

MS8

Maximum-A-Posteriori Image Registration forNoisy Data

We propose a unified framework for registration of noisyimages by modeling the unperturbed image as additionalunknown. Interpreting the motion as a linear operator onthe image we are able to derive an optimal estimation ofthe unperturbed image for any fixed transformation. Bythis we obtain specific distance measures for each transfor-mation and each data fidelity term associated to the imagenoise. We give an existence result for a wide range of datafidelity terms in case of the mass-preserving transformationoperator. Finally, we show potential advantages of the pro-posed framework by experimental evaluation on syntheticdatasets.

Sebastian SuhrMIC LubeckUniversity of Munsters [email protected]

MS8

A Gaussian Curvature Based Denoising Model forNon-Gaussian Noise.

In the last years, curvature based regularizers have becomevery popular in variational models for image denoising.However, up to our knowledge, all these models have beendesigned to deal with additive Gaussian noise only. In thiswork, we present a Gaussian curvature based model ca-pable to remove fairly both Gaussian and Non Gaussiannoise. Analisis and results of the model will be presented.

Victor Uc-Cetina, Carlos Brito-LoezaUniversidad Autonoma de [email protected], [email protected]


MS9

Anatomically Constrained Large-scale Matrix De-composition in Neuroimaging

Biomedical researchers increasingly turn to machine learn-ing methods to go beyond prior hypotheses. However, suchtools may not yield interpretable results. Prior-based eige-nanatomy addresses this concern by allowing researchers tofinely guide methods such as the singular value decompo-sition with existing hypotheses on the relationships withintheir data. We provide examples of these methods as ap-plied to MRI data and show their value for increasing pre-dictive power while retaining interpretability.

Brian AvantsImage Computing and Science LabUniversity of Pennsylvania

[email protected]

MS9

Medical Image Analysis: Applications in Need forHigh-End Computing

Modern medical imaging studies involve complex andmulti-faceted imaging data. Moreover, the problems be-ing explored become increasingly complex themselves. Wereview two problems in our computational neuroimag-ing work, which require, or can potentially require inten-sive computations: 1) generative-discriminative learning instructural neuroimaging and in functional connectomics, 2)segmentation and registration of images with tumors.

Christos DavatzikosSection of Biomedical Image Analysis, Dept. of RadiologyUniversity of [email protected]

MS9

Sparse Kaczmarz Methods - Analysis via BregmanProjections for Convex Feasibility Problems

We propose a flexible algorithmic framework to computesparse or minimal-TV solutions of linear systems. Theframework includes both the Kaczmarz method and thelinearized Bregman method as special cases and also sev-eral new methods such as a sparse Kaczmarz solver. Sincethe framework includes methods that do not work with thewhole system matrix but with subset of the rows (or evenonly single rows at a time), it can be applied to huge scaleproblems. The algorithmic framework has a variety of ap-plications and is especially useful for problems in whichthe linear measurements are slow and expensive to obtain.We present examples for online compressed sensing, TVtomographic reconstruction and radio interferometry.

Dirk LorenzTU [email protected]

MS9

Joint Methods for Reconstruction and BackgroundField Removal of QSM

Quantitative Susceptibility Mapping (QSM) is a MRI tech-nique that allows to image magnetic properties of tissue.QSM is applied increasingly, for example, in neuroscience,where iron concentration serves as a biomarker of certainneurological diseases. While the tissues susceptibility can-not be measured directly it can be reconstructed by solv-ing a highly ill-posed inverse problem. In this talk, we willpresent joint methods for QSM reconstruction as well asthe related subproblem of background field removal.

Lars RuthottoDepartment of Mathematics and Computer ScienceEmory [email protected]

MS10

A Scale-Adaptive Method for Retracing and Reg-istering in Correlative Light-Electron Microscopy

Correlative light-electron microscopy (CLEM) aims at abetter understanding of cell mechanisms by relating dy-namics with structure. However, LM and EM images

84 IS16 Abstracts

are of very different size, resolution, field-of-view, ap-pearance, usually requiring manual assistance at one orseveral stages. We have defined an original automatedCLEM retracing-and-registration method involving a com-mon representation with adaptive scale for both types ofimages, and the specification of appropriate descriptors andsimilarity criterion for the EM patch search.

Patrick Bouthemy, Bertha Mayela Toledo [email protected],[email protected]

Charles KervrannInriaRennes, [email protected]

MS10

Quantitative Cell Morphodynamics

The motility of cells is governed by a complex machineryoperating at the molecular scale, eventually translating lo-cal mechanical forces into whole-cell deformation. Here wepresent a biophysical optical flow method to extract densemaps of internal pressure and forces directly from live cellimaging data. This is achieved by mapping the motionof fluorescently labeled intracellular structures with a fluiddynamics model of the cellular material, using image analy-sis, physical modeling and mathematical optimization tech-niques.

Alexandre Dufour, Aleix Buquet, Nancy Guillen,Jean-Christophe Olivo-MarinInstitut Pasteur, Paris, [email protected], [email protected],[email protected], [email protected]

MS10

Enabling Phenotypic Screening Through ImageAnalysis

Building on robust visual tracking methods we will presentmethods for characterising cellular states, in particularthose that help to analyse different modes of cell death. Itwill be demonstrated how hierarchical Dirichlet processescan be used to identify such cellular states. In additionit will be discussed how tracking methods can be used toanalyze macrophage epithelial interactions.

Jens RittscherIBME, University of [email protected]

MS10

Shape-Constrained Tracking with Active Contours

We propose a shape-constrained tracking framework basedon active contours for the study of worm motility. Themain ingredient of our approach is the formulation of ashape space, which defines a set of admitted transforma-tions of the worm body. It allows for the decomposition ofworm motion into a collection of modes, hence giving in-sights into the nature of the different locomotion patternspresent in a dataset.

Virginie [email protected]

Daniel SchmitterBiomedical Imaging [email protected]

Michael A. [email protected]

MS11

Diffusion Tensor Imaging: Reconstruction UsingDeterministic Error Bounds

Correct noise modelling in Diffusion Tensor Imaging ischallenging: it involves the Rician distribution and thenonlinear Stejskal-Tanner equation. Linearization of thelatter in the statistical framework would complicate thenoise model even further. We propose an alternative ap-proach based on regularization in Banach lattices, whereerrors are represented as bounds by means of the appro-priate partial order and simple error structure is preservedunder monotone transformations. We present reconstruc-tion results on both synthetic and in-vivo brain data.

Yury KorolevQueen Mary University of [email protected]

Tuomo ValkonenUniversity of [email protected]

Artur GorokhCornell [email protected]

MS11

5D Respiratory Motion Model Based Image Recon-struction Algorithm for 4D Cone-Beam ComputedTomography

We aim to develop a new 4DCBCT reconstruction methodbased on 5D model. Instead of reconstructing a tempo-ral sequence of images after the projection binning, ourmethod reconstructs time-independent reference image andvector fields without requirement of binning. The formu-lated optimization problem with total-variation regulariza-tion on both reference image and vector fields is solved bythe proximal alternating minimization algorithm, of whichthe convergence analysis is provided. Validated by the sim-ulation, our method has significantly improved image re-construction accuracy due to reduced number of unknowns.

Jiulong Liu, Xue Zhang, Xiaoqun ZhangShanghai Jiao Tong [email protected], [email protected],[email protected]

Hongkai ZhaoUniversity of California, IrvineDepartment of [email protected]

Yu Gao, David ThomasUniversity of California, Los [email protected], [email protected]

Daniel Low, Hao Gao

IS16 Abstracts 85


MS11

Quantitative Ultrasound-Modulated Optical To-mography: Application of Linearised Models inPractical Imaging

Ultrasound-modulated optical tomography (UOT) is a hy-brid imaging modality which uses the spatially localisedacoustically driven modulation of coherent light as a probeof the structure and optical properties of biological tissues.A principle goal of this developing technology is the recon-struction of clinically relevant quantitative images of theabsorption and scattering coefficients of biological media,with a spatial resolution exceeding that of purely opticaltechniques such as diffuse optical tomography (DOT). Sig-nificant effort has been expended in advancing the experi-mental technique in UOT, but less attention has been paidto the fundamental problem that such hybrid techniquescan only recover quantitative images under some form ofmodel-based reconstruction procedure. In this presenta-tion I will begin by reviewing the coupled physics whichenable this modality. I will introduce various approachesto forward modelling, including a computationally efficientlinearised diffusion style formulation, solved by the finite el-ement method. I will pose the inverse problem, and exam-ine the Frchet derivatives of the forward mapping which de-fine the sensitivity of the technique. Finally, I will demon-strate two approaches to the reconstruction. In the first,I will show a simulated reconstruction using an adjoint-assisted, gradient based formulation. In the second, I willshow the use of a fully linearised reconstruction approachon experimental data acquired using photo-refractive crys-tal detection.

Samuel PowellUniversity College [email protected]

Clement Dupuy, Francois RamazEcole Superieure de Physique et de Chimie [email protected], [email protected]

Terence Leung, Simon ArridgeUniversity College [email protected], [email protected]

MS11

Primal-Dual Optimization of Phase Retrieval ViaOptimization Transfer

Optimization transfer can be used to minimize the noncon-vex phase retrieval problem via a series of minimizations ofconvex majorizer functions. These majorizers, when com-bined with variable splitting methods, provide acceleratedempirical convergence in both 1D and 2D robust phase re-trieval. This presentation will focus on primal-dual meth-ods for robust phase retrieval using both sparse regular-ization and image-domain constraints. Empirical resultsincluding Monte Carlo simulations and reconstructions ofsynthetic images will be presented.

Daniel S. WellerUniversity of Virginia

[email protected]

MS12

A Posteriori Error Control for the BinaryMumford-Shah Model

We present robust a posteriori error estimates for thearea of the non-properly segmented region in the binaryMumford-Shah model. A suitable uniformly convex andnon-constrained relaxation of the originally non-convexfunctional is investigated and Repin’s functional approachfor a posteriori error estimation is used to control the nu-merical error for the relaxed problem in the L2-norm. Incombination with a cut out argument, fully practical esti-mates for the area mismatch are derived.

Benjamin BerkelsRWTH Aachen [email protected]

Alexander Effland, Martin RumpfUniversity of BonnInstitute for Numerical [email protected], [email protected]

MS12

Adaptive Discretization of Liftings for CurvatureRegularization

Curvature regularization of image level lines is a powerfultool in image processing. Using so-called functional lift-ing, this can be achieved by specific convex functionals in ahigher-dimensional space. A major challenge in solving theresulting higher-dimensional problem are the correspond-ing high computational costs. We present an adaptive dis-cretization with a local primal-dual gap as the refinementindicator and give some results for 2D- and 3D-images.

Ulrich HartleifUniversity of MuensterEinsteinstrasse 62, 48149 Muenster, [email protected]

Benedikt WirthUniversitat [email protected]

MS12

Sublabel Accurate Lifting

We propose a novel spatially continuous framework for con-vex relaxations based on functional lifting. Our methodcan be interpreted as a sublabel-accurate solution to mul-tilabel problems. We show that previously proposed func-tional lifting methods optimize an energy which is lin-ear between two labels and hence require (often infinitely)many labels for a faithful approximation. In contrast, theproposed formulation is based on a piecewise convex ap-proximation and therefore needs far fewer labels. In com-parison to recent MRF-based approaches, our method isformulated in a spatially continuous setting and shows lessgrid bias. Moreover, in a local sense, our formulation isthe tightest possible convex relaxation. It is easy to im-plement and allows an efficient primal-dual optimizationon GPUs. We show the effectiveness of our approach on

86 IS16 Abstracts

several computer vision problems.

Emanuel LaudeTechnische Universitat Munchen, Computer VisionBoltzmannstrasse 3, 85748 Garching, [email protected]

Thomas MollenhoffTechnische Universitat [email protected]


Jan LellmannUniversity of [email protected]


MS12

Analysis L1-Minimization in Imaging

Compressive sensing predicts that sparse signals and im-ages may be recovered from incomplete information viaefficient algorithms including l1-minimization. This maybe very useful for imaging techniques such as MRI. In-stead of the standard assumption of sparsity in a basis,it is sometimes more appropriate to assume sparsity in aframe such as shearlets or curvelets. In this context, onereplaces l1-minimization by analysis-l1-minimization wherethe analysis operator is plugged into the l1-norm. This talkpresents new results on recovery of analysis-sparse imagesfrom variable density sampling of the Fourier transform.

Holger RauhutAachen [email protected]

MS13

Graph Spectral Dictionary Learning for Dis-tributed Signal Processing

We study the distributed processing of graph signals thatare well represented by graph spectral dictionaries. Wefirst analyze the impact of quantization noise in the dis-tributed computation of polynomial dictionary operatorsthat are commonly used in various signal processing tasks.We show that the impact of quantization depends on thegraph geometry and on the structure of the spectral dic-tionaries. Then, we focus on the problem of distributedsparse signal representation that can be solved with an it-erative soft thresholding algorithm. We define conditionson the dictionary structure to ensure the convergence ofthe distributed algorithm and finally propose a dictionarylearning solution that permits to control the robustness toquantization noise. Experimental results for reconstruc-tion and denoising of both synthetic and practical signalsillustrate the tradeoffs that exist between accurate signalrepresentation and robustness to quantization error in thedesign of dictionaries operators in distributed graph signalprocessing.

Pascal FrossardEPFL

EPFL - FSTI - IEL - LTS4 - Station 11, Switzerland -1015, [email protected]

Dorina [email protected]

MS13

Multiscale Geometric Methods for StatisticalLearning and Dictionaries for Data and Images

We discuss a family of ideas, algorithms, and results foranalyzing various new and classical problems in the anal-ysis of high-dimensional data sets. These methods rely onthe idea of performing suitable multiscale geometric de-compositions of the data, and exploiting such decompo-sitions to perform a variety of tasks in signal processingand statistical learning. In particular, we discuss the prob-lem of dictionary learning, where one is interested in con-structing, given a training set of signals, a set of vectors(dictionary) such that the signals admit a sparse represen-tation in terms of the dictionary vectors. We discuss amultiscale geometric construction of such dictionaries, itscomputational cost and online versions, and finite sampleguarantees on its quality. We then mention generalizationsof this construction to other tasks, such as learning an es-timator for the probability measure generating the data,again with fast algorithms with finite sample guarantees,and for learning certain types of stochastic dynamical sys-tem in high-dimensions. Applications to construction ofmulti-resolution dictionaries for images will be discussed.

Mauro MaggioniDepartment of MathematicsDuke [email protected]

MS13

Learning Separable Co-Sparse Analysis Operators- Sample Complexity and Stochastic Gradient De-scent

Analysis operator learning is referred to as learning a setof filters which, when applied to the signal class of interest,yields sparse filter responses. As such, it may serve as aprior in inverse problems, for structural analysis of images,or even for registration of bimodal images, like e.g. RGB-D. It is well known in practice that it is advantageous toconsider filters with separable structure. In this talk, wewill give an upper bound on the sample complexity for thelearning process and link this result to a stochastic gradientmethod for efficiently learning separable analysis operators.

Martin KleinsteuberDepartment of Electrical and Computer EngineeringTU [email protected]

Julian WoermannTechnical University of [email protected]

MS13

Dictionary Learning for Graph-Structured Data

One of the challenges in dictionary learning for irregularly

IS16 Abstracts 87

structured data is incorporating the intrinsic structure ofthe data into the dictionary. We present a dual graph regu-larized dictionary learning method that takes into accountthe underlying structure in both the feature and the mani-fold domains. Furthermore, we explore the dependency be-tween the dictionary and the underlying graph and proposea joint learning framework in which this graph is adaptedalongside the dictionary learning process.

Yael YankelevskyTechnion - Israel Institute of [email protected]


MS14

Inflow-Based Gradient Finite Volume Method forLevel Set Equation

We propose a cell-centered gradient defined by flux val-ues to numerically solve a propagation in normal directionon unstructured meshes. Under a suitable assumption, theproposed discretization of absolute gradient is an extensionof well-known Rouy-Tourin scheme into 3D with the secondorder upwind difference. A high order of convergence, per-formance in parallel computation, and a recovery of signeddistance function from a sparse data are illustrated in nu-merical examples.

Jooyoung HahnMathematics and Scientific ComputingUniversity of Graz, [email protected]

MS14

High Quality Image Compression Using Pde-BasedInpainting with Optimal Data

Finding good reconstruction data is a key problem forPDE-based inpainting within the context of image com-pression. Not only the location of important pixels butalso their corresponding colour values should be optimal.In this talk we discuss how the spatial and tonal optimi-sation are related and provide strategies to retrieve thisdata. Finally we present a concrete application of a lossyimage compression codec that outperforms state-of-the-artapproaches.

Laurent A. HoeltgenApplied Mathematics and Computer Vision GroupApplied Mathematics and Scientific Computing [email protected]

MS14

Mathematical Models and Numerical Methods forEarly Embryogenesis Computational Reconstruc-tion

In the talk we present mathematical models and numeri-cal methods which lead to vertebrate early embryogenesisreconstruction and extraction of the cell trajectories andthe cell lineage tree from large-scale 3D+time microscopyimage sequences. Robust and efficient numerical schemesfor solving nonlinear PDEs related to filtering, object de-tection, segmentation and tracking in 3D and 4D images

were designed, parallelized for massively parallel computerclusters and applied to the above mentioned fundamentaltasks of developmental biology. The presented results wereobtained in cooperation of groups at Slovak University ofTechnology, Bratislava, CNRS, Gif-sur-Yvette, Ecole Poly-technique, Paris and University of Bologna.

Karol MikulaDepartment of MathematicsSlovak University of [email protected]

MS14

Atlas Based Image Segmentation

The new automatic image segmentation algorithm extend-ing conventional segmentation methods with an influenceof prior knowledge of segmented shape is presented in thistalk. Algorithm is applied to Active Contours and alsoto Geodesic Active Contours method. Original contribu-tions are mainly: automatic solving of curve correspon-dence problem, registration of planar curves and estima-tion of prior shape, based on the current segmentation andcomputed eigenshapes calculated from atlas of shape pat-terns, using Principal Component Analysis.

Jozef [email protected]

MS15

Structural Priors in Image Reconstruction

Natural images exhibit geometric structures that can be ex-ploited to improve reconstruction. We propose two meth-ods that estimate the local geometry of an image and de-fine adaptive regularizers that reconstruct images of higherquality from fewer measurements. Both techniques alter-nate two steps: 1)estimation of the local image structure;2)reconstruction with a regularizer adapted to this struc-ture. This two-step procedure improves accuracy and leadsto efficient algorithms for denoising, deblurring, and com-pressed sensing.

Virgnia [email protected]

MS15

Solution-driven Adaptive Total Variation Regular-ization

In our talk we discuss adaptive variants of total variation(TV) regularization for image restoration tasks. While thestraightforward approach is to exploit the input data tosteer the adaptivity, we particularly focus on strategies,where the adaptivity is determined by the solution of theproblem (referred to as solution-driven). Our approach isdescribed in terms of a fixed-point problem, for which weprovide theory on existence and uniqueness.

Frank LenzenHeidelberg Collaboratory for Image Processing (HCI)University of [email protected]

MS15

Joint Reconstruction Via Infimal Convolution of

88 IS16 Abstracts

Bregman Distances with Applications to PET-MRImaging

Joint image reconstruction methods exploit the existenceof similar geometric structures to provide reconstructionsin presence of degraded data. We use the infimal con-volution of Bregman distances with respect to the totalvariation to couple edge information during a joint recon-struction [Moeller et al., Color Bregman TV, SIAM Jour-nal on Imaging Sciences, pp. 2771-2806, vol. 7(4), 2014.].Among theoretical results including an explicit represen-tation of the functional we present a suitable primal-dualminimization scheme. Finally, we show promising resultson artificial PET-MR data.

Julian RaschInstitute for Computational and Applied Mathematics,WWU [email protected]

Eva-Maria BrinkmannWWU [email protected]

Florian Knoll, Thomas KoestersNew York University School of [email protected], [email protected]

Frank WuebbelingWWU [email protected]

Martin BurgerUniversity of MuensterMuenster, [email protected]

MS15

Joint Hydrogeophysical Inversion Using StructureSimilarity Measures

In this study we solve a coupled hydrogeophysical inverseproblem to estimate the hydrological states. To overcomethe need to determine the relationship between geophys-ical and hydrological variables we focus on investigatingnumerical techniques which use only structure similaritymeasures, such as cross gradient field product or joint to-tal variation. Similarity measure then becomes anotherterm in the coupled objective function which also containsdata misfits and regularization terms for both hydrologicaland geophysical models.

Klara SteklovaUniversity of British ColumbiaDepartment of Earth, Ocean and Atmospheric [email protected]

Eldad HaberUniversity of British [email protected]

MS16

Sparse Representation on Non-Flat Domains withApplication in Classifications

Wavelet frames, or more generally, multiscale representa-tion of functions is well studied in the past thirty years.They have been successfully applied to various types of

practical problems, notably image processing and analysis.In recent years, it has been noted that many of the cur-rent applications in data analysis are concerned with datathat can be naturally organized on non-flat domains suchas surfaces, manifolds, point clouds and graphs. There-fore, there has been an increasing interest in constructingwavelet-like representation of functions directly on thesenon-flat domains. In this talk, I will present one of ourrecent work on generic characterization and constructionof tight wavelet frames on manifolds/graphs. Applicationsto high-dimensional classification will also be discussed.


Ning HaoDepartment of MathematicsUniversity of [email protected]

MS16

Intrinsic Methods for Image Segmentation on Man-ifolds and Extensions to Data Classification

In this talk, I will present our work on variational PDEsmethods for image segmentation on Riemannian manifolds.Based on our work of methods solving geometric PDEson manifolds, we are able to naturally generalize differentimage segment models and associated fast algorithms onRiemannian manifolds. Furthermore, I will also discuss anextension of this idea to handle general data classificationproblems.

Rongjie LaiRensselaer Polytechnic [email protected]

MS16

Fuzzy Image Segmentation Based on Tv Regular-ization and L1-Norm Fidelity

In this work, we propose a variational multiphase imagesegmentation model based on fuzzy membership functionsand L1-norm fidelity. Then we apply the alternating di-rection method of multipliers to solve an equivalent prob-lem. All the subproblems can be solved efficiently. Specifi-cally, we propose a fast method to calculate the fuzzy me-dian. Experimental results and comparisons show that theL1-norm based method is more robust to outliers such asimpulse noise and keeps better contrast than its L2-normcounterpart. Theoretically, we prove the existence of theminimizer and analyze the convergence of the algorithm.

Li FangDepartment of MathematicsEast China Normal [email protected]

Jing Qin, Jing QinUniversity of California Los [email protected], [email protected]

Stanley J. OsherUniversity of CaliforniaDepartment of [email protected]

Ming Yan

IS16 Abstracts 89

Michigan State UniversityDepartment of [email protected]

MS17

Accelerated Stochastic ADMM with Variance Re-duction

We present a novel accelerated stochastic alternating direc-tion method of multipliers(SADMM) for stochastic convexoptimization problems with linear equality constraints. Weincorporate a multi-step acceleration scheme to achieve anoptimal rate for the smooth part in the model. Our frame-work also employs variance reduction to improve the de-pendence of variance resulted by random sampling. Theefficiency of our method is demonstrated with numericalexperiments on both simulated and real data.

Chenxi Chen, Yunmei ChenDepartment of MathematicsUniversity of [email protected], [email protected]

Yuyuan OuyangDepartment of Mathematical SciencesClemson [email protected]

Eduardo Pasiliao Jr.AFRL Munitions Directorate, Air Force [email protected]

MS17

Image Reconstruction in Diffuse Optical Tomogra-phy Using Sparsity Constraint

In this talk, a sparsity constrained reconstruction formula-tion in Diffuse Optical Tomography (DOT) for determiningthe optical parameters from boundary measurements willbe presented. The sparsity of the inclusion with respectto a particular basis is assumed a priori. The proposedapproach is based on a sparsity promoting l1-penalty. Wewill present simulation results using sparsity approach inDOT.

Taufiquar R. KhanClemson [email protected]

MS17

Fast Decentralized Gradient Descent Method andApplications in Seismic Tomography

We consider the decentralized consensus optimizationproblem on a connected network where each node privatelyholds a part of objective function and data. The goal is tofind the minimizer for the whole objective function whileeach node can only communicate with its neighbors dur-ing computations. We present a fast decentralized gradientdescent method whose convergence does not require dimin-ishing step sizes as in regular decentralized gradient descentmethods, and prove that this new method can reach opti-mal convergence rate. Numerical experiments also showthat it significantly outperforms existing methods. Appli-cations to seismic tomography on large-scale wireless sensor

networks will be presented.

Xiaojing YeDepartment of Mathematics & StatisticsGeorgia State [email protected]

MS17

An Optimal Randomized Incremental GradientMethod

We present a randomized incremental gradient method andshow that it possesses unimprovable rate of convergence forconvex optimization by developing a new lower complexitybound. We provide a natural game theoretic interpretationfor this method as well as for the related Nesterov’s opti-mal method. We also point out the situations when thisrandomized algorithm can significantly outperform the de-terministic optimal method.

George LanDept of ISEUniversity of [email protected]

Yi ZhouUniversity of [email protected]

MS18

A Convex Variational Model for Restoring BlurredImages with Large Rician Noise

In this talk, a new convex variational model for restor-ing images degraded by blur and Rician noise is proposed.The new method is inspired by previous works in whichthe non-convex variational model obtained by maximum aposteriori (MAP) estimation has been presented. Based onthe statistical property of Rician noise, we put forward toadding an additional data-fidelity term into the non-convexmodel, which leads to a new strictly convex model undermild condition. Due to the convexity, the solution of thenew model is unique and independent of the initializationof the algorithm. We utilize a primal-dual algorithm tosolve the model. Numerical results are presented in theend to demonstrate that with respect to image restorationcapability and CPU-time consumption, our model has goodperformance in both medical and natural images.

Tieyong ZengDepartment of MathematicsHong Kong Baptist [email protected]

Liyuan ChenUTSouthwestern Medical [email protected]

MS18

Optimal Learning Approaches for the Determina-tion of Noise Models in Image Restoration

We aim to identify the type and structure of noise in vari-ational models by using a bilevel optimization approach.First, optimal spatially dependent weights are investigated,which yield an insight into the noise structure of the imagesat hand. Second, a new model for mixed noise is derivedconsistently with the statistical assumptions on the noise

90 IS16 Abstracts

through MAP estimation and combining standard fidelityterms used for single-noise denoising in an infimal convo-lution fashion.

Juan Carlos De los ReyesEscuela Politecnica Nacional QuitoQuito, [email protected]

Luca CalatroniCambridge Centre for AnalysisUniversity of [email protected]

Carola B. SchoenliebDAMTP, University of [email protected]

MS18

Unbiased Noise Injection in Variance-StabilizedRange

The design, optimization, and validation of many imageprocessing or image-based analysis systems often requirestesting of the system performance over a dataset of im-ages corrupted by noise at different signal-to-noise ratio(SNR) regimes. For instance, virtual clinical trials use im-ages of the same patient at different radiation doses inorder to identify the optimal dose. A noise-free ground-truth image may not be available, and different SNRs aresimulated by injecting extra noise into an already noisy im-age. We consider the additive injection of signal-dependentnoise in variance-stabilized range. In particular, we designspecial forward and inverse variance-stabilizing transfor-mations that compensate the bias which otherwise ariseswhen returning to the original range.

Lucas Borges, Marcelo VieiraUniversity of Sao [email protected], [email protected]

Alessandro FoiDepartment of Signal ProcessingTampere University of Technology, [email protected]

MS18

Noise Estimation Based on a Non-Parametric De-tection of Homogeneous Image Regions

We propose a two-step algorithm that automatically es-timates the noise level function of stationary noise froma single image, i.e., the noise variance as a function ofthe image intensity. First, the image is divided into smallsquare regions and a non-parametric test is applied to de-cide whether each region is homogeneous or not. Basedon Kendall’s τ coefficient (a rank-based measure of corre-lation), this detector has a non-detection rate independenton the unknown distribution of the noise, provided that itis at least spatially uncorrelated. Moreover, we prove on atoy example, that its overall detection error vanishes withrespect to the region size as soon as the signal to noise ratiolevel is non-zero. Once homogeneous regions are detected,the noise level function is estimated as a second order poly-nomial minimizing the �1 error on the statistics of theseregions. Numerical experiments show the efficiency of theproposed approach in estimating the noise level function.

We illustrate the interest of the approach for an image de-noising application.

Camille SutourUniversity of [email protected]

MS19

Automatic Detection of Heart Anomalies in Car-diac Ultrasound Data

We consider the problem of automatic classification ofheart defects from cardiac ultrasound. Currently this imag-ing modality is used by expert physicians in the diagnosis ofpatients with heart abnormalities. With the advent of au-tomation in image processing and machine learning tools itmay be possible to use such devices to continuously monitorpatients in hospital settings where it would not be practicalto have an expert cardiologist on hand at all times. Such amonitoring device requires continuous automated process-ing of the data to alert hospital staff about changes in thepatient’s status. In this talk we discuss possible ways ofdoing this using a combination of imagine processing as apreprocessing step for machine learning tools to separateout different classes of patients.


Stamatios [email protected]

MS19

A Fast Solver for Constrained Diffeomorphic ImageRegistration

We present new algorithms for diffeomorphic image reg-istration. We use a PDE-constrained formulation, wherethe constraints are the transport equations for the tem-plate image. We introduce a semi-Lagrangian formula-tion and a two-level coarse grid Hessian preconditioner,which—in combination with a globalized, matrix-free, in-exact Newton–Krylov method—results in an orders of mag-nitude speed-up over the state of the art.

Andreas MangThe University of Texas at AustinThe Institute for Computational Engineering and [email protected]

George BirosThe Institute for Computational Engineering and SciencesThe University of Texas at [email protected]

MS19

Efficient Lung CT Registration Using Large Defor-mation Diffeomorphic Metric Mappings

The topic of the talk is 3D lung CT image registration us-ing the Large Deformations Diffeomorphic Metric MappingMethod (LDDMM) method. It is well known that LD-DMM has large memory requirements as flows over timeare modeled. We will discuss techniques to handle thischallenge for the registration of full resolution lung CTscans. Furthermore, we will talk about changing the dis-

IS16 Abstracts 91

tance measure to Normalized Gradient Fields to cope withinhale-exhale scans.

Thomas PolzinInstitute of Mathematics and Image ComputingUniversity of [email protected]

MS19

Diffeomorphic Image Matching and the Choice ofthe Metric

In medical image applications, diffeomorphic image match-ing has been extensively developed and variational meth-ods are among the most often used. Usually, these methodsconsist in the minimization of an energy which is the sum oftwo terms, a similarity measure and a regularization on thedeformation. For instance, in the so-called large deforma-tion diffeomorphic metric mapping, a differential operatorhas to be chosen usually via a regularizing kernel, which isalso the case in the framework of stationary velocity fields.The choice of the regularizing term has an important im-pact on the results of the methods, namely the registrationitself, and as a consequence on further analysis that can bebuilt upon. In this talk, we will present some propositionsto improve the choice of the regularization and in partic-ular we will present a variational framework to learn theregularization from the data.

Francois-Xavier VialardUniversite [email protected]

MS20

Inferring Causality in Molecular Processes UsingLive Cell Microscopy

One of the challenges in the study of complex molecularpathways is adaptation of the system to experimental per-turbation. While perturbation of one component may leadto an observable phenotype, it is impossible to deduce fromit the function the targeted component. To overcome thisproblem we exploit basal pathway fluctuations observedby live cell imaging and employ time series analysis ap-proaches to reconstruct the connectivity and kinetics ofinformation flows between pathway components.

Gaudenz DanuserUT Southwestern Medical [email protected]

MS20

Computational Imaging Methods to Study CardiacDevelopment and Function

Optical microscopy allows observing cardiac developmentin zebrafish larvae, which offer direct optical access tomigrating cardiac cells, tissue reorganization and bloodflow within the beating heart. This dynamic environmentmakes imaging and analysis of individual components chal-lenging. We have developed methodologies based on accu-rate temporal registration of movies of the beating heartthat allow leveraging its quasi-periodic beat to separateimage components, computationally improve the temporalresolution of the movies as well as their signal to noise.

Nikhil ChackoUniversity of California Santa Barbara

[email protected]

Kevin G. ChanUniversity of California Santa Barbaraand [email protected]

Sandeep K. Bhat, Jungho OhnUniversity of California Santa [email protected], [email protected]

Michael [email protected]

MS20

Quantitative Aspects of the Analysis of Superreso-lution and Single Molecule Experiments

Image analysis is a central component of single moleculebased super resolution microscopy. For example, in lo-calization based super resolution microscopy the improve-ment in resolution over conventional techniques dependscrucially on the quality of the image analysis. The analysisof imaging experiments for dynamics in three dimensionshas particular challenges. We will discuss recent resultsthat illustrate the use of information theory for experimentdesign and the evaluation of image analysis approaches.

Raimund J. OberUniversity of Texas at DallasCtr of Engineering [email protected]

MS20

Tracking and Registration for Analyzing Live CellMicroscopy Images

We present approaches for cell tracking, particle tracking,and registration of dynamic cell microscopy images. We de-veloped an approach for cell tracking and cell cycle quantifi-cation which integrates tracking-by-detection, mitosis de-tection, feature-based classification, and error correctionusing a state transition model. For analyzing the motionof virus particles, we introduced a probabilistic trackingapproach based on particle filters and Kalman filters. Wealso developed non-rigid registration approaches for spatialnormalization of the image data.

Karl RohrUniversity of [email protected]

MS21

Photoacoustic Imaging and Thermodynamic At-tenuation

We consider a mathematical model for photoacoustic imag-ing to take into account attenuation due to thermodynamicdissipation. The propagation of acoustic waves is governedby a scalar wave equation coupled to the heat equationfor the excess temperature. We seek to recover the ini-tial acoustic profile from knowledge of boundary measure-ments. This inverse problem is a special case of boundaryobservability for a thermoelastic system. This leads to theuse of control/observability tools to prove the unique andstable recovery of the initial acoustic profile in the weak

92 IS16 Abstracts

thermoelastic coupling regime. We propose and implement(numerically) a reconstruction algorithm.

Sebastian AcostaBaylor College of [email protected]

MS21

Optoacoustic Tomography of the Breast: ImageReconstruction and Signal Detectability

Optoacoustic tomography (OAT) is an emerging hybridmethod for clinical breast imaging. In this talk, we describethe development and evaluation of advanced optimization-based image reconstruction methods for OAT. These meth-ods account for the instrument response and imagingphysics. Concepts from statistical decision theory are em-ployed to quantify image quality based on a signal detectiontask.

Mark A. AnastasioDept. of Biomedical EngineeringIllinois Institute of [email protected]

Yuan LouDepartment of Biomedical EngineeringWashington University in St. [email protected]

Alexander OraevskyTomoWave [email protected]

MS21

A Dissipative Time Reversal Technique for Photo-acoustic Tomography in a Cavity

We consider the inverse source problem arising in thermo-and photoacoustic tomography. It consists in reconstruct-ing the initial pressure from the boundary measurementsof the acoustic wave. Our goal is to extend versatile timereversal techniques to the case when the boundary of thedomain is perfectly reflecting, effectively turning the do-main into a reverberant cavity. Standard time reversalworks only if the solution of the direct problem decays intime, which does not happen in the setup we consider. Inthis talk, we propose a novel time reversal technique witha non-standard boundary condition. The error induced bythis time reversal technique satisfies the wave equation witha dissipative boundary condition and, therefore, decays intime. For larger measurement times, this method yields aclose approximation; for smaller times, the first approxi-mation can be iteratively refined, resulting in a convergentNeumann series for the approximation.

Linh NguyenUniversity of [email protected]

Leonid A. KunyanskyUniversity of ArizonaDepartment of [email protected]

MS21

Thermo-Acoustic Tomography on Bounded Do-

mains

We study the mathematical model of thermoacoustic to-mography in bounded domains with perfect reflectingboundary conditions. We propose an averaged time re-versal (ATR) algorithm which solves the problem with anexponentially converging Neumann series. Numerical re-construction based on this ATR algorithm is implementedand compared with the reconstruction using the Landwe-ber iteration algorithm. This is based on joint work withPlamen Stefanov.

yang YangDepartment of MathematicsPurdue [email protected]

MS22

ShapeFit: Exact Location Recovery from Cor-rupted Pairwise Directions

We consider the problem of recovering a set of locationsgiven observations of the direction between pairs of theselocations. This task arises from the Structure from Motionproblem from machine vision, in which 3d structure is to beinferred from 2d images. We introduce a tractable convexprogram called ShapeFit and prove that it can recover asynthetic set of locations exactly when a fraction of themeasurements are adversarially corrupted.

Paul HandRice [email protected]

Choongbum Lee, Vladislav VoroninskiMITcb [email protected], [email protected]

MS22

Probably Certifiably Correct K-Means Clustering

Recently, Bandeira introduced a new type of algorithm (theso-called probably certifiably correct algorithm) that com-bines fast solvers with the optimality certificates providedby convex relaxations. This talk introduces such an al-gorithm for the problem of k-means clustering. First, weobserve that a certain semidefinite relaxation of k-means istight with high probability under a certain distribution ofplanted clusters. Next, we show how to test the optimalityof a proposed k-means solution using the relaxation’s dualcertificate in quasilinear time. (Joint work with TakayukiIguchi, Jesse Peterson and Soledad Villar.)

Dustin MixonAir Force Institute of [email protected]

MS22

Robust Camera Location Estimation by ConvexProgramming

3D structure recovery from a collection of 2D images re-quires the estimation of the camera locations and orienta-tions, i.e. the camera motion. For large, irregular collec-tions of images, existing methods for the location estima-tion part, which can be formulated as the inverse problemof estimating n locations t1, t2, . . . , tn in R3 from noisy

measurements of a subset of the pairwise directionsti−tj

‖ti−tj‖ ,

IS16 Abstracts 93

are sensitive to outliers in direction measurements. In ourwork, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by pre-senting its relation to the existing theory of parallel rigidity.For robust estimation of camera locations, we introduce atwo-step approach, comprised of a pairwise direction esti-mation method robust to outliers in point correspondencesbetween image pairs, and a convex program to maintain ro-bustness to outlier directions. In the presence of partiallycorrupted measurements, we empirically demonstrate thatour convex formulation can even recover the locations ex-actly. Lastly, we demonstrate the utility of our formula-tions through experiments on Internet photo collections.

Onur [email protected]

Amit SingerPrinceton [email protected]

MS22

Efficient Global Solutions to K-Means ClusteringVia Semidefinite Relaxation

k-means clustering aims to partition a set of n points intok clusters in such a way that each observation belongs tothe cluster with the nearest mean, and such that the sumof squared distances from each point to its nearest meanis minimal. In the worst case, this is a hard optimizationproblem, requiring an exhaustive search over all possiblepartitions of the data into k clusters in order to find theoptimal clustering. At the same time, fast heuristic algo-rithms for k-means are often applied, despite only beingguaranteed to converge to local minimizers of the k-meansobjective. Here, we consider a semidefinite programmingrelaxation of the k-means optimization problem. We dis-cuss two regimes where the SDP provides an algorithmwith improved clustering guarantees compared to previousresults in the literature: (a) for points drawn from isotropicdistributions supported in separated balls, the SDP recov-ers the globally optimal k-means clustering under mild sep-aration conditions; (b) for points drawn from mixtures ofdistributions with bounded variance, the SDP solution canbe rounded to a clustering which is guaranteed to classifyall but a small fraction of the points correctly. This talkis based on papers Relax no need to round: integralityof clustering formulations (joint work with P. Awasthi, A.Bandeira, M. Charikar, R. Krishnaswamy and R. Ward)and Clustering subgaussian mixtures by semidefinite pro-gramming (joint work with D. Mixon and R. Ward).

Soledad VillarUniversity of Texas at [email protected]

MS23

Functorial Metric Clustering with Overlaps: Pos-sibilities and Impossibilities

It is natural to attempt extending the range of functorialdissimilarity-based clustering methods beyond partitionsand dendrograms (as introduced by Carlsson and Memoli)to allow the treatment of clustering with overlaps. We char-acterize the possible domains of classifiers (combinatoriallyand metrically), and derive a common generalization ofKleinberg’s impossibility result and the Carlsson-Memoli

characterizations of single linkage hierarchical clustering.We also explore connections between functorial clusteringand the split-decomposition/projection methods of Bune-mann and Bandelt-Dress.

Dan [email protected]

Jared CulbertsonAir Force Research [email protected]

Peter F. StillerTexas A&M [email protected]

MS23

A Matching Algorithm for Reducing Complexes inMultidimensional Persistence

An algorithm is presented that constructs an acyclic par-tial matching on the cells of a given simplicial complexfrom a vector-valued function defined on the vertices. Theresulting acyclic partial matching is used to construct a re-duced complex with the same multidimensional persistenthomology as the original complex filtered by sublevel setsof the function. Numerical tests on triangle meshes showthat the achieved rate of reduction is substantial.

Claudia LandiUniversity of Modena and Reggio [email protected]

Madjid AlliliBishop’s UniversitySherbrooke, [email protected]

Tomasz KaczynskiUniversite de SherbrookeQuebec (Canada)[email protected]

MS23

Persistence Weighted Gaussian Kernel for Topo-logical Data Analysis

In topological data analysis(TDA), persistence diagramsare widely used to describe the robust and noisy topologi-cal properties in data. In this talk, I will propose a kernelmethod on persistence diagrams to develop a statisticalframework in TDA. Then, a new distance on persistencediagrams is defined by our kernel and has a stability prop-erty. The main contribution of our method is the flexibilityto control the effect of persistence. As an application, weshow that our method can clearly detect the glass transi-tion temperature in SiO2.

Genki KusanoTohoku [email protected]

MS23

Multiscale Mapper: Topological SummarizationVia Codomain Covers

Summarizing topological information from datasets and

94 IS16 Abstracts

maps defined on them is a central theme in topological dataanalysis. Mapper, a tool for such summarization, takes asinput both a possibly high dimensional dataset and a mapdefined on the data, and produces a summary of the databy using a cover of the codomain of the map. This cover,via a pullback operation to the domain, produces a sim-plicial complex connecting the data points. The resultingview of the data through a cover of the codomain offersflexibility in analyzing the data. However, it offers only aview at a fixed scale at which the cover is constructed.Inspired by the concept, we explore a notion of a tower ofcovers which induces a tower of simplicial complexes con-nected by simplicial maps, which we call multiscale map-per. We study the resulting structure, and design practicalalgorithms to compute its persistence diagrams efficiently.Specifically, when the domain is a simplicial complex andthe map is a real-valued piecewise-linear function, the algo-rithm can compute the exact persistence diagram only fromthe 1-skeleton of the input complex. For general maps, wepresent a combinatorial version of the algorithm that actsonly on vertex sets connected by the 1-skeleton graph, andthis algorithm approximates the exact persistence diagramthanks to a stability result that we show to hold.

Facundo MemoliOhio State [email protected]

MS24

Low-complexity Semidefinite Programming Meth-ods and Applications in Computer Vision

Semidefinite programming is a classical method for relaxingnon-convex problems into convex problems. In this talk,we present alternatives that relax non-convex and discreteproblems into a bi-convex form. This alternative methodallows us to solve very large-scale semidefinite programswith extremely low complexity. Applications to image seg-mentation and machine learning will be discussed.

Tom GoldsteinDepartment of Computer ScienceUniversity of [email protected]

Christoph StuderCornell [email protected]

Sohil Shah, Abhay KumarUniversity of [email protected], [email protected]

MS24

Ingredients for Computationally Efficient DiffuseOptical Tomographic Reconstruction

In diffuse optical tomography the goal is to reconstructa map of the absorption and/or diffusion coefficient frommeasurements on the surface. The forward model is thediffusion equation, which makes the problem computation-ally challenging. We describe how to combine paramet-ric level sets (PaLS) with a trust region regularized GNapproach and model order reduction to bring the compu-tational costs down dramatically. We show results thathighlight the success of the combined approach.

Misha E. KilmerMathematics Department

Tufts [email protected]

Eric De SturlerVirginia [email protected]

Serkan GugercinVirginia Tech.Department of [email protected]

Christopher A. BeattieVirginia Polytechnic Institute and State [email protected]

Meghan O’ConnellDepartment of MathematicsTufts [email protected]

MS24

A Direct Reconstruction Method for AnisotropicElectrical Impedance Tomography

Electrical Impedance Tomography (EIT), also known asElectrical Resistance Tomography (ERT) is a relativelynew imaging technique that is non-invasive, low-cost, andnon-ionizing with excellent temporal resolution. In geo-physics, EIT data consists of electrical boundary measure-ments, of voltages measured on electrodes arising from ap-plied currents on the electrodes, that are used to deter-mine the unknown electrical condutivity in the interior ofthe medium. EIT has wide variety of applications includ-ing medical imaging and geophysical prospecting. Thistalk presents a direct reconstruction scheme for 2-D esti-mation of an anisotropic conductivity from EIT data thatincludes prior knowledge of the anisotropy tensor. The lin-earized Calderon–based scheme makes use of a special typeof CGO solutions known as Oscillating Decaying solutionsto a related problem to recover the spatially dependentanisotropic conductivity values.

Rashmi MurthyDepartment of MathematicsColorado State [email protected]

Jennifer L. MuellerColorado State UniversityDept of [email protected]

MS24

Sparsity in Fluids - Vorticity Estimation via Com-pressive Sensing

In recent years compressive sensing has been applied suc-cessfully to various imaging problems where sparsity ininformative basis structures played a key role. In fluids,vortex methods (e.g. Rankine or Lamb-Oseen) were usedto model the evolution of flows related to Navier-Stokes.The aim of this talk is to present a new model combiningcompressive sensing and vortex methods for fluid problemsin imaging. Besides an analysis of approximations in thelimiting case we will highlight numerical results for vortic-ity estimation in image sequences motivated by eddies in

IS16 Abstracts 95

oceanic sciences.

Hui SunUniversity of California San [email protected]

Christoph BruneDepartment of Applied MathematicsUniversity of [email protected]


MS25

A Scalable Space-Time Multiresolution Model forActivation and Connectivity in Fmri Data


Stefano CastruccioUniversity of [email protected]

MS25

Modeling and Data Visualization of Electroen-cephalograms


Hernando OmbaoUniversity of California, [email protected]

MS25

Structural Connectivity: Challenges and FutureOutlook


Hongtu ZhuUniversity of North [email protected]

MS26

How the Brain Represents Images: Biologically In-spired Algorithms for Classification and Recogni-tion

Making inferences from partial information constitutes aubiquitous and fundamental aspect of intelligence. Ourbrains constantly complete patterns in the context of in-terpreting speech and narratives, when discerning socialinteractions or when visually analyzing scenes. I will dis-cuss the problem of pattern completion during recognitionof heavily occluded objects. The type of extrapolation re-quired to complete occluded objects is not trivial. Givenan image containing an occluded object, there are infinitepossible ways to interpret and complete the image. Yet,the brain is capable of typically and rapidly landing on asingle interpretation. I will present behavioral and physi-ological data constraining possible solutions. Next, I willpresent a computational model that combines a bottom-uphierarchical architecture with recurrent connectivity. Thismodel displays many of the interesting pattern recogni-tion properties of deep convolutional networks and at the

same type has attractor states that allow the system to dy-namically modify the representation when presented withpartial information. The proposed biological plausible cir-cuits provide initial steps to elucidate the mechanisms bywhich the brain can extrapolate and make inferences fromminimal information.

Gabriel KreimanHarvard [email protected]

MS26

Lagrangian Transforms for Signal and Image Clas-sification

Invertible image representation methods (transforms) areroutinely employed as low-level image processing opera-tions based on which feature extraction and recognitionalgorithms are developed. Most transforms in current use(e.g., Fourier, Wavelet, etc.) are linear transforms, and, bythemselves, are unable to substantially simplify the repre-sentation of image classes for classification. Here we de-scribe a nonlinear, invertible, low-level image processingtransform based on combining the well known Radon trans-form for image data, and the 1D Cumulative DistributionTransform proposed earlier. We describe a few of the prop-erties of this new transform, and with both theoretical andexperimental results show that it can often render certainproblems linearly separable in transform space.

Gustavo K. Rohde, Se Rim ParkCarnegie Mellon [email protected], [email protected]

MS26

Scotopic Recognition - The Dark Side of Vision

Images are obtained by counting the photons that hit asensor within a given amount of time. Thus, ‘images’ area convenient engineering abstraction. In the real worldthere are only individual photons traveling through spaceand hitting a pixel at a given time. I will discuss how vi-sion can be formulated in the context of such a stream ofphotons, without ever forming a conventional image. Thishas practical importance: in many applications only fewphotons are available and decisions have to be made asquickly as possible - just when the sufficient amount ofinformation has been captured. Examples are biomedicalimaging, security, astronomy. I will discuss a frameworkthat allows a machine to classify objects with as few pho-tons as possible, while maintaining the error rate below anacceptable threshold. The framework also allows for a dy-namic and asymptotically optimal speed-accuracy tradeoff.I will briefly touch upon detection and control applicationsas well.

Pietro Perona, Bo ChenCalifornia Institute of [email protected], [email protected]

MS26

Adaptive Piecewise Data Representation: Learn-ing Manifolds and Dictionaries

In this talk, I will discuss a class of algorithms to learndata representation from unsupervised data. The class ofproposed methods exploit the geometry of the data distri-bution to build piecewise data representations. Analyzing

96 IS16 Abstracts

their performance requires tools from geometry and proba-bility, with connection to diverse ideas such as vector quan-tization, wavelets, and decision trees.

Lorenzo RosascoInstituto Italiano di Technologia andMassachusetts Institute of [email protected]

MS27

Data Refactoring: Using Auditors for Next Gener-ation Storage Systems

Common compression schemes are limited for scientific dueto under-utilization of apriori domain knowledge. We pro-pose a new scheme, an auditor, which exploits this addi-tional knowledge. An auditor performs a low cost computa-tion to track the data over a spatio-temporal interval. Thedifference from the auditors results and the actual datais stored as entropy coded deltas alongside the auditorsparameters. This combination allows the data to be regen-erated at machine precision while approaching the optimalcompression ratio. The dual layer structure of the com-pressed data is also ideal for modern storage hierarchies,allowing variable precision access to data.

Scott KlaskyOak Ridge National LaboratoryOak Ridge, [email protected]

MS27

Parallel Tensor Compression for Large-Scale Scien-tific Data

As parallel computing trends towards the exascale, scien-tific data produced by high-fidelity simulations are growingincreasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension thattracks 64 variables per grid point for 128 time steps yields8 TB of data. By viewing the data as a dense five-waytensor, we can compute a Tucker decomposition to findinherent low-dimensional multilinear structure, achievingcompression ratios of up to 10000 on real-world data setswith negligible loss in accuracy. So that we can operateon such massive data, we present the first-ever distributed-memory parallel implementation for the Tucker decomposi-tion, whose key computations correspond to parallel linearalgebra operations, albeit with nonstandard data layouts.Our approach specifies a data distribution for tensors thatavoids any tensor data redistribution, either locally or inparallel. We provide accompanying analysis of the com-putation and communication costs of the algorithms. Todemonstrate the compression and accuracy of the method,we apply our approach to real-world data sets from com-bustion science simulations. We also provide detailed per-formance results, including parallel performance in bothweak and strong scaling experiments.

Woody N. AustinUniversity of Texas - [email protected]

Grey Ballard, Tamara G. KoldaSandia National Laboratories


MS27

Compressed Floating-Point Arrays for High-Performance Computing

We present zfp: a compressed floating-point array prim-itive that supports a user-specified storage budget andhigh-speed read and write random access. zfp arrays useC++ operator overloading to mimic regular multidimen-sional C++ arrays, which facilitates application integra-tion. We demonstrate several use cases of zfp arrays inhigh-performance computing applications, including inlinecompression of simulation state and streaming compres-sion that reduces I/O and disk storage by up to 100 timeswithout compromising visual quality.

Peter LindstromLawrence Livermore National [email protected]

MS27

Compressed Sensing and Reconstruction of Un-structured Mesh Datasets: Optimal Compression

We investigate Compressive Sensing (CS) as a method tocompress scientific simulation data. CS works by samplingthe data on the computational cluster within an alterna-tive function space, then reconstructing back to the orig-inal space on visualization platforms. While much workhas gone into exploring CS on structured datasets, we in-vestigate its usefulness for point-clouds such as unstruc-tured mesh datasets. We achieve compression ratios up to100 with minimal visual deterioration in the reconstructeddata.

Maher SalloumSandia National LaboratoriesScalable and Secure Systems Research [email protected]

Nathan FabianSandia National LaboratoriesScalable Analysis and [email protected]

David Hensinger, Jeremy TempletonSandia National [email protected], [email protected]

Elizabeth AllendorfUniversity of California, Los [email protected]

MS28

Sparse Sampling Methods for Neutron Tomogra-phy

This talk will focus on mathematics developed to help withthe mathematical challenges face by the DOE at the ex-perimental facilities. This talk will discuss sparse sam-pling methods and fast optimization developed specificallyfor neutron tomography. Sparse sampling has the abil-ity to provide accurate reconstructions of data and imageswhen only partial information is available for measurement.Sparse sampling methods have demonstrated to be robustto measurement error. These methods have the potential

IS16 Abstracts 97

to scale to large computational machines and analysis largevolumes of data.

Rick [email protected]

MS28

Total Fractional-Order Variation Regularisationand Its Applications

We analyse and develop a fractional-order derivative basednonlocal regulariser, which can outperform the currentlypopular high order regularization models and has been usedto substantially reduce the staircase effect of the total vari-ation based model. Two new frameworks of noise removingin image restoration and nonlocal deformation in non-rigidimage registration are presented. Numerical experimentsshow that the proposed models can produce highly com-petitive results.


Jianping Zhang, Bryan WilliamsUniversity of LiverpoolLiverpool, [email protected],[email protected]

MS28

Parsing Local Signal Evolution Directly fromSingle-shot MRI Data Using a Second Order Ap-proximation in Time

Most current methods of MRI reconstruction interpret sig-nal as samples of the Fourier transform. Although this iscomputationally convenient, it neglects relaxation and off-resonance evolution in phase, both of which can occur toa significant extent during typical MR data acquisition. Amore accurate model (SS-PARSE) takes the time evolu-tion of the signal into consideration. Our reconstructionscheme for such models relies on decomposing the signalinto time-frames and �1 regularization.

Rodrigo B. PlatteArizona State [email protected]

MS28

Fast Robust Phase Retrieval from Local Correla-tion Measurements

Certain imaging applications such as x-ray crystallographyrequire the recovery of a signal from magnitude-only mea-surements. This is a challenging problem since the phaseencapsulates a significant amount of structure in the under-lying signal. In this talk, we develop an essentially linear-time algorithm for solving the discrete phase retrieval prob-lem using local correlation measurements. We present the-oretical guarantees and numerical results demonstratingthe method’s speed, accuracy and robustness.

Mark IwenMichigan State [email protected]

Aditya ViswanathanArizona State [email protected]

MS29

Multi-GPU Strategies for Computing Frame Based3D Reconstructions in Cone-Beam CT

Frame-based methods for cone beam tomography result initerative schemes demanding high-performance computingstrategies, particularly in the context of system optimiza-tion and image quality studies. Two issues must be ad-dressed: fast projections and memory management for re-dundant expansions. Multi-GPU systems are a convenientway to leverage thousands of cores and dozens of gigabytesof memory to address both issues. We discuss a multi-GPU implementation and demonstrate its applicability toan image quality study.

Nick HenscheidUniversity of [email protected]

MS29

Sparsity-Exploiting Image Reconstruction for Vol-ume Ct Using Algorithms with Truncated IterationNumber

Optimization-based image reconstruction for CT is com-putationally expensive. Only first-order algorithms areavailable for solving optimization problems of interest ac-curately, requiring thousands of iterations. In practice, itis desirable to operate at 10 or less iterations. Accuratesolution is not possible with such low iteration numbers,but it is still possible to achieve high quality volume re-constructions with such a constraint. We will present al-gorithm designs exploiting image gradient sparsity, whichcan provide useful images within ≈ 10 iterations.

Emil SidkyDepartment of RadiologyThe University of [email protected]

Ingrid Reiser, Xiaochuan PanThe University of ChicagoDepartment of [email protected], [email protected]

MS29

Iterative Reconstruction for Practical InteriorProblems in X-Ray Tomography Using a Dual GridMethod

In many practical non-medical x-ray CT applications, itis often the case that the measured projection data areseverely truncated, creating a problem of extreme interiortomography. To accurately reconstruct such datasets us-ing iterative methods, it is necessary for the reconstructiongrid to cover the entire object support, creating infeasiblecomputational and memory demands. We present a sim-ple dual grid approach to mitigate these demands, withcomputational burden of only approximately double thenon-truncated case.

William ThompsonCarl Zeiss X-ray Microscopy Inc.

98 IS16 Abstracts

[email protected]

MS29

Fast Prototyping of Advanced Tomographic Recon-struction Algorithms

The need for advanced reconstruction techniques in tomog-raphy is growing and it has become computationally feasi-ble to apply such techniques to large tomographic datasets.However, coupling complicated algorithms to existing (highperformance) codes is often challenging and currently ham-pers their application in practice. Since these algorithmsoften require only simple operations of the forward op-erator (multiplication, transpose) we propose an abstractlinear operator framework for tomographic reconstruction.With this framework, the algorithm can be developed witha generic linear operator in mind, while the underlyingcomputations can be handled by highly optimized code.Such a framework has the added benefit that individualcomponents can be tested separately, thus guaranteeing thefidelity of the resulting code. We present a specific exam-ple in Matlab, where we use a high-end GPU tomographytoolbox as backend.

Tristan van LeeuwenMathematical InstituteUtrecht [email protected]

Folkert Folkert Bleichrodt, Joost BatenburgCentrum Wiskunde en [email protected], [email protected]

MS30

Non-Unique Games Over Compact Groups andOrientation Estimation in Cryo-Em

Let G be a compact group and let fij ∈ L2(G). Wedefine the Non-Unique Games (NUG) problem as findingg1, . . . , gn ∈ G to minimize

∑ni,j=1 fij(gig

−1j ). We devise

a relaxation of the NUG problem to a semidefinite pro-gram (SDP) by taking the Fourier transform of fij over G,which can then be solved efficiently. The NUG frameworkcan be seen as a generalization of the little Grothendieckproblem over the orthogonal group and the Unique Gamesproblem, and includes many practically relevant problems,such as the maximum likelihood estimator to registeringbandlimited functions over the unit sphere in d-dimensionsand orientation estimation in cryo-Electron Microscopy.

Afonso S. [email protected]

Yutong Chen, Amit SingerPrinceton [email protected], [email protected]

MS30

Algorithmic and Computational Challenges in Sin-gle Particle Reconstruction

I will give a short introduction to the modern algorithmicand computational challenges in single particle reconstruc-tion using cryo-electron microscopy. I will discuss someof the approaches that are currently being employed, andexplain why and how tools from different branches of math-ematics such as representation theory, random matrix the-

ory, and convex optimization play an important role inadvancing this imaging technique.


MS30

Orthogonal Matrix Retrieval in Cryo-Electron Mi-croscopy

In single particle reconstruction (SPR) from cryo-electronmicroscopy (EM), the 3D structure of a molecule needsto be determined from its 2D projection images taken atunknown viewing directions. Zvi Kam showed already in1980 that the autocorrelation function of the 3D moleculeover the rotation group SO(3) can be estimated from 2Dprojection images whose viewing directions are uniformlydistributed over the sphere. The autocorrelation functiondetermines the expansion coefficients of the 3D moleculein spherical harmonics up to an orthogonal matrix of size(2l + 1) × (2l + 1) for each l=0,1,2... We will show howtechniques for solving the phase retrieval problem in X-raycrystallography can be modified for the cryo-EM setup forretrieving the missing orthogonal matrices. Specifically, wepresent two new approaches that we term Orthogonal Ex-tension and Orthogonal Replacement, in which the mainalgorithmic components are the singular value decomposi-tion and semidefinite programming. We demonstrate theutility of these approaches through numerical experimentson simulated data.

Teng ZhangUniversity of Central [email protected]

MS30

Fast Steerble Principal Component Analysis

Cryo-electron microscopy nowadays often requires theanalysis of hundreds of thousands of 2D images as largeas a few hundred pixels in each direction. Here we in-troduce an algorithm that efficiently and accurately per-forms principal component analysis (PCA) for a large setof two-dimensional images, and, for each image, the setof its uniform rotations in the plane and their reflections.For a dataset consisting of n images of size LL pixels, thecomputational complexity of our algorithm is O(nL3 +L4).

Zhizhen ZhaoCourant Institute of Mathematical SciencesNew York [email protected]

MS31

An Inverse Problem of Combined Photoacousticand Optical Coherence Tomography

Photoacoustic and optical coherence tomography areemerging non-invasive biological and medical imaging tech-niques. However, it is well known by now that withoutadditional assumptions on the medium, it is not possibleto uniquely reconstruct all physical parameters from eitherone of these modalities alone. As both methods give infor-mation about the light propagation in the medium (photoa-coustics involving mainly the absorption, optical coherencetomography mainly the scattering properties), they com-plement each other and thus a combined experiment per-

IS16 Abstracts 99

forming photoacoustic and optical coherence tomographyat once could provide enough data to make a quantitativereconstruction possible. In this talk, we want to present amathematical model for this dual experiment and show in asimplified setting that we can uniquely recover all physicalparameters.

Peter ElbauUniversity of [email protected]

Leonidas Mindrinos, Otmar ScherzerComputational Science CenterUniversity [email protected], [email protected]

MS31

Lorentz Force Impedance Tomography in 2D

Lorentz Force tomography, aslo known as Magneto-Acousto-Electric Tomography (MAET), is a novel hybridmodality that represents a stable, high-resolution alterna-tive to the Electrical Impedance Tomography (EIT). Sim-ilar to EIT, MAET aims at imaging the non-uniform con-ductivity inside an object. To this end the object is placedin a magnetic field and subjected to ultrasound waves. Thecharged particles moving in a magnetic field a subjected bythe Lorentz force, which generates currents that are thenmeasured outside of the object. After a short theoreticalintroduction into MAET, I will present the design of a pro-totype MAET scanner we have built, and will demonstratesome of the first MAET images ever obtained.

Leonid A. KunyanskyUniversity of ArizonaDepartment of [email protected]

MS31

Stability and Statistics for Shear Stiffness Imaging


Joyce R. McLaughlinRensselaer Polytechnic InstDept of Mathematical [email protected]

MS31

Quantitative Pat for Molecular Imaging

Fluorescence photoacoustic tomography (fPAT) is a molec-ular imaging modality that combines photoacoustic tomog-raphy (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside het-erogeneous media. The objective of this work is to studyinverse problems in the quantitative step of fPAT wherewe intend to reconstruct physical coefficients in a cou-pled system of radiative transport equations using internaldata recovered from ultrasound measurements. We deriveuniqueness and stability results on the inverse problemsand develop some efficient algorithms for image reconstruc-tions. Numerical simulations based on synthetic data arepresented to validate the theoretical analysis.

Yimin Zhong, Kui Ren, Rongting ZhangUniversity of Texas at Austin

[email protected], [email protected],[email protected]

MS32

Novel Algorithms for Vectorial Total Variation

While Total Variation is an extremely popular regularizerfor scalar-valued functions, there exists a multitude of pos-sible generalizations to the vector-valued setting. In mytalk, I will introduce some recent developments which makeuse of geometric measure theory and �p,q,r-norms in orderto derive a unified framework for vectorial total variationmodels. A detailed analysis and experimental evaluationof the arising models reveals which ones are best suited forcolor image denoising and other inverse problems.


Bastian GoldlueckeDepartment of Computer ScienceUniversity of [email protected]

Evgeny StrekalovskiyTechnical University of [email protected]


Joan DuranUniversity of Balearic Islands, [email protected]

Thomas MollenhoffTechnical University of Munich, [email protected]

MS32

A Generalized Forward-Backward Splitting

This work introduces a generalized forward-backward split-ting algorithm for finding the zeros of the sum of maximalmonotone operators A+

∑ni=1 Bi on Hilbert space, where A

is also co-coercive. While the forward-backward algorithmdeals only with n = 1 operator, our method generalizes itto the case of arbitrary n. Our method makes an explicituse of the co-coercivity of A in the forward (explicit) stepand the resolvents of Bi’s are activated separately in thebackward (implicit) step. We establish (weak and strong)convergence properties of our algorithm as well as its ro-bustness to summable errors in the implicit and explicitsteps. We then specialize the algorithm for the case of com-posite variational problems to minimize convex functionsof the generic form f +

∑ni=1 gi, where f has a Lipschitz-

continuous gradient and the gi’s are simple. Applicationsto inverse problems in imaging demonstrate the advantageof the proposed framework.

Jalal FadiliCNRS, ENSICAEN-Univ. of Caen, [email protected]

Hugo Raguet

100 IS16 Abstracts

Ceremade CNRS-Universite [email protected]

Gabriel PeyreCNRS, CEREMADE, Universite [email protected]

MS32

Coherence Pattern-Guided Compressive Sensingwith Unresolved Grids

Highly coherent sensing matrices arise in discretizing witha grid spacing below the Rayleigh threshold or representingthe objects by a highly redundant dictionary. Compressedsensing algorithms based on techniques of band exclusionand local optimization can circumvent coherent or redun-dant sensing matrices and accurately reconstruct sparseobjects separated by up to one Rayleigh length indepen-dent of the grid spacing.

Albert Fannjiang, Wenjing LiaoUC [email protected], [email protected]

MS32

PhaseLift: Exact Phase Retrieval via Convex Pro-gramming

We present a novel framework for phase retrieval, a prob-lem arising in Xray-crystallography, diffraction imagingand many other applications. Our framework, calledPhaseLift, combines multiple structured illuminations to-gether with ideas from convex programming to recover thephase from intensity measurements. PhaseLift also comeswith theoretical guarantees for exact and stable recovery,and can be modified to exploit sparsity. We will overviewsome of the many new developments since PhaseLift in thephase-retrieval and related communities.

Emmanuel CandesStanford UniversityDepartments of Mathematics and of [email protected]

Yonina C. EldarTechnion and [email protected]

Thomas StrohmerUniversity of California,DavisDepartment of [email protected]

Vladislav [email protected]

MS33

The Unexpected Geometry of ”Real” High-Dimensional Data

We describe a surprising property of high-dimensional datasets, which we first observed while studying large sets ofimages and subsequently found in many other “real” datasets as well. Our observations suggest that real high-dimensional data sets have a tremendous amount of struc-ture, so much so that a mere projection onto a random1D subspace of the data space is likely to uncover some of

that structure. This has important implications in the areaof automatic recognition and database indexing. For ex-ample, we have developed an ultra-fast method based onrandom 1D projections for clustering a high-dimensionaldata set. Note that, if the data points had been drawnfrom a mixture of Gaussians (or any other density func-tion representing clusters in the traditional sense) in theinitial high-dimensional space, then the data could not ef-fectively be clustered using such method. Thus the geome-try at hand is a lot more complex than previously thought.This work is in collaboration with my graduate studentSangchun Han (now at Google).

Mireille BoutinSchool of ECEPurdue [email protected]

MS33

A Variational Approach to the Consistency of Spec-tral Clustering

We consider clustering of point clouds obtained as samplesof a ground-truth measure. A graph representing the pointcloud is obtained by assigning weights to edges based on thedistance between the points they connect. We investigatethe spectral convergence of both unnormalized and normal-ized graph Laplacians towards the appropriate operators inthe continuum domain. We obtain sharp conditions on howthe connectivity radius can be scaled with respect to thenumber of sample points for the spectral convergence tohold. In addition, we show that the discrete clusters in-duced by the spectrum of the graph Laplacian, convergestowards a continuum partition of the ground truth mea-sure. Such continuum partition minimizes a functional de-scribing the continuum analogue of the graph-based spec-tral partitioning.

Nicolas Garcia Trillos, Dejan SlepcevCarnegie Mellon Universitynicolas garcia [email protected], [email protected]

MS33

Layered Diffusion: Towards a Theory of Intercon-nected Networks

Real world social networks consist of agents (as nodes) withassociated states, and connected through complex topolo-gies. Such an instance may include, for example, informa-tion sources accessed by agents which are themselves inter-connected and follow some dynamics and hence evolve overtime. In this work we propose a novel network model witha tractable hierarchical and interconnected structure, withlearned diffusion dynamics subsequently exploited in thetracking and prediction of future states of each node

Hamid KrimNorth Carolina State UniversityElectrical and Computer Engineering [email protected]

Shahin AghdamNorth Carolina State [email protected]

Han [email protected]

IS16 Abstracts 101

Liyi DaiArmy Research [email protected]

MS33

On Geometric Problems in Structure from Motion


Gilad LermanUniversity of Minnesota, MinneapolisSchool of [email protected]

MS34

Phase Tracking: Interpretation of Seismic Recordsin Terms of Atomic Events

Interpretation of seismic shot records in terms of coher-ent atomic events can be formulated as a hard, nonconvexoptimization problem. I will present a method that em-pirically finds the global minimum of this functional in thecase of simple synthetic shot records, even when eventscross. The idea is to slowly grow a trust region for phasesand amplitudes in a way that reminds of continuation, ortracking. The ability to solve this problem has importantimplications for low-frequency extrapolation and full wave-form inversion. Joint work with Yunyue Elita Li.

Laurent DemanetDepartment of Mathematics, [email protected]

Yunyue LiMassachusetts Institute of [email protected]

MS34

Joint Inversion of Gravity Data and Seismic Trav-eltimes Using a Structural Parametrization

We propose a structural approach for the joint inversionof gravity data and seismic traveltimes. Two geophysi-cal properties including the density contrast and the seis-mic slowness are simultaneously inverted in the inverseproblem. We develop a level set parametrization to main-tain the structural similarity between multiple geophysicalproperties. Since density and slowness are different modelparameters of the same survey domain, we assume thatthey are similar in structure in terms of how each prop-erty changes and where the interface exists, and we use thelevel set function to parameterize the common interfaceshared by these two model parameters. The interpretationof gravity data and seismic data are coupled by minimizinga joint data-fitting function with respect to the density dis-tribution, the slowness distribution as well as the level setfunction. An adjoint state method is incorporated in theoptimization algorithm to handle the non-linear constraintarisen from traveltime tomography. We test our algorithmin plenty of numerical examples, including the 2-D ovoidmodel and the SEG/EAGE salt model. The results showthat the joint-inversion algorithm signicantly improves re-covery of the subsurface features.

Wenbin Li, Jianliang QianDepartment of MathematicsMichigan State University


MS34

Frozen Gaussian Approximation and Its Applica-tions

We propose the frozen Gaussian approximation for thecomputation of high frequency wave propagation. Thismethod approximates the solution to the wave equationby an integral representation. It provides a highly efficientcomputational tool based on the asymptotic analysis onphase plane. Compared to geometric optics, it provides avalid solution around caustics. Compared to the Gaussianbeam method, it overcomes the drawback of beam spread-ing. We will present numerical examples as well as prelim-inary application in seismology to show the performance ofthis method.

Xu YangDepartment of MathematicsUniversity of California, Santa [email protected]

MS35

On Local and Non Local Covariant Derivatives andTheir Applications in Color Image Processing

The Euclidean gradient operator and its non-local exten-sion are involved in many variational models used in im-age analysis and processing. We present a generalizationof these operators and variational models by replacing thestandard differentiation of functions on the Euclidean spaceby the covariant differentiation of sections on a vector bun-dle, a geometric structure generalizing the concept of man-ifold. We show the efficiency of the generalization proposedfor image denoising and contrast reduction/enhancement.

Thomas BatardDepartment of Information and CommunicationsTechnologiesUniversity Pompeu [email protected]

Marcelo BertalmıoUniversitat Pompeu [email protected]

MS35

Locally Adaptive Frames in the Roto-TranslationGroup SE(d)

Locally adaptive differential frames are used in differen-tial invariants and PDE-flows on d-dimensional images.However, at complex structures, these frames are not well-defined. Therefore, we propose locally adaptive frameson (invertible) data representations defined on the coupledspace of positions and orientations SE(d)/({0} × SO(d −1)). This allows for multiple well-defined frames per posi-tion, one for each orientation. We compute these framesvia local exponential curve fits to the data. Applications in-clude improved crossing-preserving vesselness filtering anddiffusions.

Remco DuitsIST/eEindhoven University of [email protected]

102 IS16 Abstracts

Michiel JanssenDepartment of Mathematics and Computer ScienceEindhoven University of [email protected]

MS35

Locally Rigid Averaging of stretchable non-rigidshapes

We present a new approach for generating the mean struc-ture of non-rigid stretchable shapes. Such structure is thenused for inferring normal and abnormal characteristics ofa given population. Following an alignment process, whichsupports local affine deformations, we translate the searchof the mean shape into a diagonalization problem wherethe structure is hidden within the kernel of a matrix. Thisapproach is fast, robust, and is suitable for stretchablenon-rigid structures, unrelated to their global coordinateframes.


Eduardo Bayro-CorrochanoCinvestav Unidad Guadalajara, [email protected]

Ramesh RaskarMassachusetts Institute of [email protected]

MS35

On the Geometry of Shading and Color

We consider the shape-from-shading inference problem onimage patches modelled with Taylor polynomials of any or-der. A boot-strapping tensor framework and generic con-straint allows us to relate a smooth image patch to all ofthe polynomial surface solutions (under any light source).Color flows impact material judgements.

Steven ZuckerYale UniversityComputer Science and Electrical [email protected]

Benjamin KunsbergBrown [email protected]

Daniel [email protected]

MS36

Spectral Decompositions Via One-HomogeneousRegularization Functionals

To analyze linear filters for image and signal analysis, onetypically considers the spectral decomposition of the corre-sponding linear operator. This talk discusses the possibilityto introduce similar concepts for nonlinear transformationsarising from the solution of variational, scale space, or in-verse scale space methods. In particular, the possibilityto decompose input data in into a linear combination ofgeneralized eigenvectors with respect to one-homogeneous

regularization functionals will be presented.

Michael MollerTechnical University [email protected]

Guy GilboaElectrical Engineering DepartmentTechnion IIT, Haifa, [email protected]


MS36

A Dirichlet Energy Criterion for Graph-Based Im-age Segmentation

We consider a graph-based approach for image segmen-tation. We introduce several novel graph constructionmodels which are based on graph-based segmentation cri-teria extending beyond—and bridging the gap between—segmentation approaches based on edges and homogeneousregions alone. The resulting graph is partitioned using acriterion based on the sum of the minimal Dirichlet energiesof partition components. We propose an efficient primal-dual method for computing the Dirichlet energy groundstate of partition components and a rearrangement algo-rithm is used to improve graph partitions. The methodis applied to a number of example segmentation problems.We demonstrate the graph partitioning method on the five-moons toy problem, and illustrate the various imagebasedgraph constructions, before successfully running a varietyof region-, edge-, hybrid, and texture-based image segmen-tation experiments. Our method seamlessly generalizesregion- and edge-based image segmentation to the multi-phase case and can intrinsically deal with image bias aswell.

Braxton OstingUniversity of [email protected]

Dominique ZossoUniversity of California, Los AngelesDepartment of [email protected]

MS36

Fundamentals of Non-Local Total Variation Spec-tral Theory

Eigenvalue analysis based on linear operators has beenextensively used in signal and image processing to solvea variety of problems such as segmentation, dimensional-ity reduction and more. Recently, nonlinear spectral ap-proaches, based on the total variation functional have beenproposed. In this context, functions for which the nonlin-ear eigenvalue problem λu ∈ ∂J(u) admits solutions, arestudied. When u is the characteristic function of a set A,then it is called a calibrable set. If λ > 0 is a solutionof the above problem, then 1/λ can be interpreted as thescale of A. However, this notion of scale remains local,and it may not be adapted for non-local features. For thiswe introduce in this paper the definition of non-local scalerelated to the non-local total variation functional. In par-ticular, we investigate sets that evolve with constant speed

IS16 Abstracts 103

under the non-local total variation flow. We prove thatnon-local calibrable sets have this property. We proposean onion peel construction to build such sets. We eventu-ally confirm our mathematical analysis with some simplenumerical experiments.

Nicolas Papadakis

CNRS/[email protected]

Jean-Francois AujolIMB, CNRS, Universite Bordeaux [email protected]


MS36

Multiscale Segmentation via Bregman Distancesand Spectral TV Analysis

In biomedical imaging the automatic detection of objects ofinterest is a key problem to solve. In this talk we addressthe strong need for automatic and reliable segmentationmethods by a robust, TV-based multiscale framework. Weextent the forward scale-space by an inverse approach us-ing Bregman iterations. A particular focus is the detectionof multiple scales using spectral decomposition recently in-troduced for TV. Results for simulated and experimentalcell data illustrate the methods effectiveness.

Leonie ZeuneUniversity of [email protected]


MS37

Direct Sampling Methods for Electrical ImpedanceTomography and Diffusive Optical Tomography

In this talk, we are concerned with the electrical impedancetomography (EIT) and the diffusive optical tomography(DOT) in the case when only one or two pairs of Cauchydata are available, which are known to be very difficultin achieving high reconstruction quality owing to theirseverely ill-posed nature. We propose simple and efficientdirect sampling methods (DSM) to locate inhomogeneitiesinside a homogeneous background and attempt the two to-mographies in both full and limited aperture cases. Fol-lowing the pioneering works by Ito, Jin and Zou, we havenow extended this method, which is originally only appli-cable to the inverse acoustic medium scattering problem,to a much wider class of severely ill-posed inverse prob-lems, e.g. DOT and EIT. In each of the aforementionedtomography, a new family of probing functions is intro-duced to construct an indicator function for imaging theinclusions, which is defined as a dual product between theobserved data and the probing functions under an appro-priate choice of Sobolev scale. The newly proposed DSMsare easy to implement and computationally cheap. Numer-ical experiments are presented to illustrate its robustnessagainst noise in the data, and its extremely effective in lo-

cating small abnormalities. This provides a new promisingnumerical strategy for solving the various problems in theinverse problem community.

Yat Tin ChowUniversity of California, Los [email protected]

Kazufumi ItoNorth Carolina State UniversityDepartment of [email protected]

Keji LiuShanghai University of Finance and [email protected]

Jun ZouThe Chinese Univ. of Hong [email protected]

MS37

Compressed Sensing and Reconstruction of Un-structured Mesh Datasets: Performance and Ac-curacy

We show in-progess results from our Lab Directed Re-search and Development work with Compressive Sensing(CS) using second-generation wavelets to compress simula-tion data. With emphasis on in-situ, we examine impactson performance and accuracy by compressing, with loss,while the simulation is running and then decompressingduring post-processing. We will show the effects on simu-lation runtime, overall time to solution, and errors inducedby the lossy compression. We compare CS with other pop-ular compression schemes.

Nathan FabianSandia National LaboratoriesScalable Analysis and [email protected]

Jina Lee, David HensingerSandia National [email protected], [email protected]

Maher SalloumSandia National LaboratoriesScalable and Secure Systems Research [email protected]

MS37

Multi-Node Model-Based Image Reconstructionwith GPUs

Model-based X-ray CT image reconstruction is normallyperformed by solving a computationally expensive numer-ical optimization problem with a large amount of data.The data size poses a challenge for any GPU implemen-tation, where memory is often limited. We present a fastduality-based algorithm that interleaves memory transfersand computation to mitigate this problem. To handle evenlarger reconstructions, we extend this algorithm to multipleGPUs on a node and multiple network-connected nodes.

Madison G. McGaffin, Jeffrey FesslerUniversity of Michigan

104 IS16 Abstracts


MS37

Arock: an Algorithmic Framework for Asyn-chronous Parallel Coordinate Updates

Finding a fixed point to a nonexpansive operator, i.e.,x∗ = Tx∗, abstracts many problems in numerical linearalgebra, optimization, and other areas of scientific com-puting. To solve fixed-point problems, we propose ARock,an algorithmic framework in which multiple agents (ma-chines, processors, or cores) update x in an asynchronousparallel fashion. Asynchrony is crucial to parallel com-puting since it reduces synchronization wait, relaxes com-munication bottleneck, and thus speeds up computing sig-nificantly. At each step of ARock, an agent updates arandomly selected coordinate xi based on possibly out-of-date information on x. The agents share x through eitherglobal memory or communication. If writing xi is atomic,the agents can read and write x without memory locks.Theoretically, we show that if the nonexpansive operatorT has a fixed point, then with probability one, ARock gen-erates a sequence that converges to a fixed points of T .Our conditions on T and step sizes are weaker than com-parable work. Linear convergence is also obtained. Wepropose special cases of ARock for linear systems, convexoptimization, machine learning, as well as distributed anddecentralized consensus problems. Numerical experimentsof solving sparse logistic regression problems are presented.

Zhimin PengUniversity of California. Los AngelesDepartment of [email protected]




MS38

Multiscale Sparse Representations in VariationalImage Reconstruction

In many problems of image reconstruction we encounterthe issue of dealing with incomplete or corrupted data.Often the most efficient recovery models are tailored forspecific classes of images. Our work is merging the modelsand methods of the applied harmonic analysis, compressivesensing and variational techniques to create highly adapt-able methods for image analysis and reconstruction. Pre-liminary analysis of the image determines the presence ofedges and dominant directions, if those exist. The oper-ators designed based on this information are used in thevariational image reconstruction. The efficiency of this ap-proach is illustrated with numerical examples of denoisingand inpainting of images from various classes.

Julia DobrosotskayaCase Western Reserve University

[email protected]

MS38

A Novel Fidelity and Regularity for Image Recon-struction

We propose a general framework for image reconstruction.The contributions are two-fold: instead of the traditionalfidelity in measurement domain, we measure the closenessin a processing domain; for regularity, we selectively chooseTV and fractional-order total variation in different regionsto fuse the power and avoid drawbacks of each individual.Image measurements are projected onto one frame domainwhile regularizing the solution in another domain. Nu-merical experiments in non-uniform Fourier reconstructionshow its advantages.


Yue ZhangCase Western Reserve [email protected]

Guohui SongClarkson [email protected]

MS38

A novel Backtracking Strategy for AcceleratedADMM and Applications to Image Reconstruction

In this talk, we propose a novel line search basedaccelerated alternating direction method of multiplier(ADMM) scheme for solving regularized large-scale andill-conditioned linear inversion problems. The proposedscheme can be viewed as the accelerated alternating direc-tion method of multiplier (AADMM) [Ouyang, etc.] witha relaxed line search condition. It allows more aggressivestepsize via conducting fewer number of line searches thanthat in AADMM to achieve better practical performance,while preserves the same accelerated rate of convergence asthat for AADMM. Experimental results on total-variationbased image reconstruction indicate the efficiency of theproposed algorithm.

Xianqi LiDepartment of MathematicsUniversity of [email protected]

MS39

Predicting Performance of Sparsity-Regularized X-Ray Tomography: Experimental Results usingGlass-Bead Data

Compressive sensing connects the undersampling level al-lowed by sparsity regularization to the sparsity level of theimage. Our recent work with simulated data indicates asimilar connection in X-ray tomography. This may allowone to predict how many projections will suffice for accu-rate reconstruction. In this talk we address validation withreal micro-CT data of different-sized glass beads specifi-cally acquired for the purpose. We describe the experi-

IS16 Abstracts 105

ment, first results and discuss implications.

Jakob JorgensenTechnical University of [email protected]

MS39

Development of Reconstruction Algorithms ofPractical Utility in Sparse-Data X-Ray Tomo-graphic Imaging


Xiaochuan PanThe University of ChicagoDepartment of [email protected]

MS39

fMRI Reconstruction Using a State Estimation Ap-proach

Functional magnetic resonance imaging (fMRI) is an imag-ing modality that is widely used to study physiological pro-cesses. However, many of these processes occur too fast foradequate reconstruction by conventional approaches. Inthis talk we formulate the fMRI image reconstruction asa state estimation problem, where the highly under sam-pled data is complemented with both temporal and spatialprior information. The approach is tested with simulatedand measured fMRI data.

Ville-Veikko WettenhoviUniversity of Eastern [email protected]

MS40

Classification of Cryo-Em Projections Using Low-Rank Covariance Estimation


Joakim AndenPrinceton [email protected]

MS40

Elucidating Protein Structure at High Resolutionby Cryo-EM: Advances and Challenges

Recent advances in the field of single particle cryo-electronmicroscopy (cryo-EM) have enabled the determination ofprotein structure at unprecedented atomic resolution. Im-provements in electron detector technology as well as ad-vances in image processing have contributed significantlyto this achievement. Here, we present an overview of recentdevelopments in the cryo-EM field and outline the manychallenges still remaining of working with time-resolved ex-tremely low SNR images of radiation sensitive biologicalspecimens.

Alberto Bartesaghi

NCI / [email protected]

MS40

Wavelet Frame Based Algorithm for 3D Recon-

struction in Electron Microscopy

In electron microscopy, three-dimensional (3D) reconstruc-tion is one key component in many computerized tech-niques for solving 3D structures of large protein assembliesusing electron microscopy images of particles. Main chal-lenges in 3D reconstruction include very low signal-to-noiseratio and very large scale of data sets involved in the com-putation. In this talk, we presented a wavelet tight framebased 3D reconstruction approach that exploits the spar-sity of the 3D density map in a wavelet tight frame system.The proposed approach not only runs efficiently in a termsof CPU time but also requires a much lower memory foot-print than existing framelet-based regularization methods.The convergence of the proposed iterative scheme and thefunctional it minimizes is also examined, together with theconnection to existing wavelet frame based regularizations.The numerical experiments showed good performance ofthe proposed method when it is used in two electron mi-croscopy techniques: the single particle method and elec-tron tomography.

Hui JiNational University of [email protected]

MS40

Fast Algorithms for 3D Cryo-Em Reconstruction

Image reconstruction in cryo-electron microscopy is a com-putationally intensive process. Not only does it give riseto a non-convex optimization problem, the raw data is ex-tremely noisy. Existing methods are generally based onsome version of the expectation maximization method tosolve a maximum likelihood problem, with a low resolutionstarting guess. We will present a collection of algorithmsintended to accelerate the reconstruction - some based onfast algorithms for the computation of putative projectionsfrom the current model of the molecule, some based on ac-celerated fitting of data to that model and some based ona recursion in frequency that mitigates the difficulties as-sociated with the non-convexity of the optimization task.

Marina SpivakSimons [email protected]

MS41

Inverse Schroedinger Problem with Internal Mea-surements

We consider the problem of finding the Schrodinger po-tential from a few measurements of solutions to theSchrodinger equation corresponding to different sourceterms. This problem arises in hydraulic tomography wherethe goal is to image the hydraulic properties of an aquiferby injecting water in one well and measuring the change inpressure in other wells.

Fernando Guevara VasquezUniversity of [email protected]

MS41

Nonlinear Acoustic Imaging via Reduced OrderModel Backprojection

We introduce a novel nonlinear acoustic imaging methodbased on model order reduction. The reduced order model

106 IS16 Abstracts

(ROM) is an orthogonal projection of the wave equationpropagator on the subspace of snapshots of solutions ofthe acoustic wave equation. It can be computed entirelyfrom the knowledge of the time domain data. The image isa backprojection of the ROM using the subspace basis for aknown smooth kinematic velocity model. Implicit orthog-onalization of solution snapshots is a nonlinear procedurethat differentiates our approach from the conventional lin-ear methods (Kirchhoff, reverse time migration - RTM).It allows for automatic removal of multiple reflection arti-facts. It also doubles the resolution in range compared toconventional RTM.

Alexander V. MamonovUniversity of [email protected]

Vladimir L. DruskinSchlumberger-Doll [email protected]

Andrew E. ThalerInstitute for Mathematics and its [email protected]

Mikhail ZaslavskySchlumberger-Doll [email protected]

MS41

Stability from Partial Data in Current DensityBased Impedance Imaging

I will present some recent progress on the stability prob-lem in Current Density based Impedance Imaging (CDII)from partial data. This work explains the resolution andaccuracy obtained in CDII pictures in the case of partialinterior and boundary data. This is joint work with CarlosMontalto of University of Washington.

Carlos MontaltoUniversity of [email protected]

Alexandru TamasanUniversity of Central [email protected]

MS42

Multistatic Imaging of Extended Targets

We develop iterative approaches for imaging extended in-clusions from multistatic response measurements at singleor multiple frequencies. Assuming measurement noise, weperform a detailed stability and resolution analysis of theproposed algorithms in two different asymptotic regimes:the Born approximation in the nonmagnetic case and ahigh-frequency regime in the general case. This talk isbased on the paper H. Ammari, J. Garnier, H. Kang, M.Lim, and K. Solna, SIIMS, 5, 564-600 (2012).

Habib AmmariEcole Normale [email protected]

Josselin GarnierUniversity Paris DiderotLaboratoire de Probabilites et Modeles Aleatoires

[email protected]

Hyeonbae KangDepartment of Mathematics, Inha [email protected]

Mikyoung LimDept. of Mathematical SciencesKAIST, [email protected]

Knut SolnaUniversity of California at [email protected]

MS42

Fast Alternating Direction Optimization Methods

This talk will discuss recent advances in ADMM/SplitBregman methods for problems in imaging and machinelearning. Will will focus on the application of Nesterov-type acceleration to achieve fast convergence rates. Wewill discuss a number of applications in distributed com-puting, machine learning, and image processing.

Tom GoldsteinDepartment of Computer ScienceUniversity of [email protected]

Brendan O’DonoghueGoogle [email protected]

Simon SetzerSaarland University, [email protected]

Richard BaraniukRice [email protected]

MS42

Some Recent Advances in Primal-Dual Methodsfor Saddle-Point Problems

We showed that the primal-dual hybrid gradient (PDHG)method can be explained from the proximal point algo-rithm (PPA) perspective, and the work was published onSIIMS in 2012. This fact has enabled us to find moreresults of this important method, including the under-standing of its convergence when one function of a saddle-point problem is strongly convex, the design an algorithmicframework of generalized PDHG methods, and the conver-gence analysis of some inexact versions of PDHG. I willpresent some of our recent results in this talk.

Bingsheng HeNanjing University, [email protected]

Xiaoming YuanDepartment of MathematicsHong Kong Baptist University

IS16 Abstracts 107

[email protected]

MS42

Image Denoising Using Mean Curvature of ImageSurface

We will discuss a variational model for image denoisingusing the L1-norm of mean curvature of the image graphas a regularizer. Besides eliminating noise and preservingedges, the model can keep image contrasts and sharp cor-ners, and also remove the staircase effect. We will alsoaddress a fast algorithm for the model using augmentedLagrangian methods. Numerical experiments will be pre-sented to show the features of the model. Recent progresswill also be reported.

Wei ZhuMathematics, University of [email protected]

Tony [email protected]

MS43

Effective Algebra and Geometry for Images withVaried Topology

Topological summaries of geometric data, such as multipa-rameter persistent homology extracted from medical andbiological images, require interpretable data structures forsubsequent statistical analysis to proceed. Combinatorialcommutative algebra provides a language to encode thesesummaries that clarifies the topological interpretation andilluminates potential pitfalls of the topological techniquesbut also indicates effective methods to overcome them. Themain dataset leading to these developments consists of pho-tographic images of fruit fly wings with varying topologicalpatterns of veins, but the principles and data structures aregeneral for multiparameter persistence.

Ezra MillerDepartment of MathematicsDuke [email protected]

Ashleigh ThomasDuke UniversityDepartment of [email protected]

MS43

Local-to-Global Homology and Barcode Fields

Persistent homology lets us construct informative topolog-ical summaries of the shape of data. Using a kernel con-struction, we propose a localized form of homology rep-resented by a continuous barcode field that is stable withrespect to the Wasserstein metric and thus robust to noiseand outliers. We also discuss applications to genetics ofplant morphology.

Washington Mio, Mao LiDepartment of MathematicsFlorida State University


MS43

Directional Features, Projective Coordinates andClassification

Directional features in images have been shown to be fun-damental in digit recognition and texture classificationtasks. We will show in this talk how projective spaces canbe used to model distributions of said features, and howdata can be mapped onto these spaces.

Jose PereaDuke [email protected]

MS43

Topologically Accurate Digital Image Analysis Us-ing Discrete Morse Theory

Our work with x-ray micro-CT images of complex porousmaterials has required the development of topologicallyvalid and efficient algorithms for studying and quantify-ing their intricate structure. For example, simulations oftwo-phase fluid displacements in a porous rock depend onnetwork models that accurately reflect the connectivity andgeometry of the pore-space. These network models areusually derived from curve-skeletons and watershed basins.Existing algorithms compute these separately and may giveinconsistent results. We have shown that Forman’s discreteMorse theory, informed by persistent homology, providesa unifying framework for simultaneously producing topo-logically faithful skeletons and compatible pore-space par-titions. Our code package, diamorse, for computing theseskeletons, partitions and persistence diagrams is now avail-able on GitHub. The code contains several optimisationsthat allow it to process images with up to 20003 voxels ona high-end desktop PC.

Vanessa Robins, Olaf [email protected],[email protected]

Adrian SheppardAustralian National [email protected]

MS44

Geometrical Learning and Cardinal Composition ofShape Elements in Imaging and Vision

The problem of interest is learning the main geometriccomponents of a target object with reference to a dictio-nary of prototype shapes. The object characterization isthrough the composition of matching elements from theshape dictionary. The composition model allows set unionand difference among the selected elements, while regu-larizing the problem by restricting their count to a fixedlevel. Convex cardinal shape composition (CSC) is a re-cent relaxation scheme to address this combinatorial prob-lem. We discuss general sufficient conditions under whichCSC identifies a target composition. We provide qualita-tive results on how well the CSC outcome approximatesthe combinatorial solution. We also propose a fast con-vex solver to address the problem. Applications vary frommulti-resolution image segmentation, and recovery of theprincipal shape components, to optical overlapping char-

108 IS16 Abstracts

acter recognition.

Alireza AghasiMIT Media [email protected]

Justin RombergSchool of ECEGeorgia [email protected]

MS44

Prior Model Identification During Subsurface FlowData Integration with Adaptive Sparse Represen-tations


Behnam JafarpourDepartment of Chemical Engineering and [email protected]

MS44

Compressive Conjugate Directions: Linear Theory

We present a powerful and easy-to-implement iterativealgorithm for solving large-scale optimization problemsthat involve L1/total-variation (TV) regularization. Themethod is based on combining the Alternating DirectionsMethod of Multipliers (ADMM) with a Conjugate Direc-tions technique in a way that allows reusing conjugatesearch directions constructed by the algorithm across mul-tiple iterations of the ADMM. The new method achievesfast convergence by trading off multiple applications of themodeling operator for the increased memory requirementof storing previous conjugate directions. We illustrate thenew method with a series of imaging and inversion appli-cations.

Musa MaharramovExxonMobil Upstream Research [email protected]

Stewart LevinDepartment of GeophysicsStanford [email protected]

MS45

Fringe Analysis Using Curvature Models

The main goal of fringe analysis techniques is to recoveraccurately the local modulated phase from one or severalfringe patterns; such phase is related to some physicalquantities, such as shape, deformation, refractive index,and temperature. In this talk, we introduce a curvaturebased variational model for computing discontinuous phasemaps from fringe patterns. The analisys of the model andits performance on experiments with both synthetic andreal data are presented.

Carlos Brito-LoezaAutonomous University of [email protected]

Ricardo Legarda-Saenz

Universidad Autonoma de [email protected]

MS45

Image Comparison Via Group Invariant Non-Expansive Operators

Two images are often judged equivalent if they are obtainedfrom each other by applying a transformation belonging toa given group G of homeomorphisms (e.g., the group ofisometries). In this talk we illustrate a G-invariant methodfor metric comparison of grey-level images represented byreal-valued functions. This approach is based on the ap-plication of group invariant non-expansive operators to theimages and on the computation of the corresponding per-sistent homology.

Patrizio FrosiniUniversity of BolognaDipartimento di [email protected]

MS45

Variational Frequencies Multiscale Models and theGeneration of Nonlinear Eigenfunctions

Recent studies of convex functionals and their relatedeigenvalue problems show surprising analogies to harmonicanalysis based on classical transforms (e.g. Fourier). Thusnew types of models and processing algorithms can be de-signs, such as ones based on the Total-Variation Transform.This talk will further investigate the atoms of regularizerswhere a flow which can generate a large variety of nonlin-ear eigenfunctions and pseudo-eigenfunctions will be intro-duced, shining light on examples yet unknown.

Raz NossekTechnion, Haifa, [email protected]


MS45

A Computational Model of Amodal Completion

We present a computational model that gives the mostlikely scene interpretation from a planar image; the inter-pretation includes both the disoccluded objects and theirordering according to depth. We use a Bayesian modelwhich depends on the global complexity of the objects con-forming the scene plus the effort of bringing them together.To compute the disoccluded objects we use a geometric in-painting method based on Eulers elastica, relatability andconvexity.

Maria OliverDepartment of Information and CommunicationsTechnologiesUniversity Pompeu [email protected]

Gloria HaroUniversitat Pompeu [email protected]

IS16 Abstracts 109

Mariella DimiccoliCentre de Visio per Computadorfirst name

Baptiste MazinDxO Labsfirst name

Coloma BallesterUniversitat Pompeu [email protected]

MS46

Variational Motion Estimation for Cell Migration

Our aim is to track and to analyze migrating leukocytes.Therefore, we use 4d in vivo fluorescence microscopy data,which offers a variety of mathematical challenges. We per-form a combination of registration, segmentation and flowestimation, whereas the latter will be the focus of this talk.To detect the intracellular and extracellular motion of thecells, we present ideas for variational flow models that com-bine the abilities to recover smooth transitions and sharpedges.

Lena FrerkingUniversity of [email protected]



Dietmar VestweberMPI Molecular Biomedicine, [email protected]

MS46

Precise Relaxation for Motion Estimation

Variational motion estimation problems, such as opticalflow and depth from stereo, often exhibit highly irregularand nonconvex data terms. Lifting-based convex relaxationmethods promise to find good minimizers by approximat-ing the original energy. However, their resolution has so farbeen limited by the number of artificial labels, and obtain-ing accurate solutions requires to solve very large problems.In this talk, we present a strategy for precisely relaxingnon-convex energies in a way that allows to find accuratesolutions that are not limited by the number of labels. Thisgreatly reduces the problem size and makes application tomany real-world problems feasible. We demonstrate theusefulness on several variational problems in the context ofimage restoration and motion estimation.

Jan LellmannUniversity of [email protected]

Emanuel LaudeTechnische Universitat Munchen, Computer Vision

Boltzmannstrasse 3, 85748 Garching, [email protected]

Thomas MollenhoffTechnical University of Munich, [email protected]



MS46

Adaptive Regularization of the Non-Local Meansfor Video Denoising

We derive a denoising method based on an adaptive reg-ularization of the non-local means. The NL-means reducenoise by using the redundancy in natural images. Theycompute a weighted average of pixels whose surroundingsare close. This reduces significantly the noise while preserv-ing most of the image content. While it performs well onflat areas and textures, it suffers from two opposite draw-backs: it might over-smooth low-contrasted areas or leavea residual noise around edges and singular structures. Weintroduce a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-meansby adaptively regularizing non-local methods with the to-tal variation. We use the weights computed in the NL-means as a measure of performance of the denoising pro-cess. These weights balance the data-fidelity term in anadapted ROF model, in order to locally perform adaptiveTV regularization. Besides, this model can be adaptedto different noise statistics and a fast resolution can becomputed in the general case of the exponential family.We adapt this model to video denoising by using spatio-temporal patches. Compared to spatial patches, they offerbetter temporal stability, while the adaptive TV regular-ization corrects the residual noise observed around movingstructures.

Camille SutourUniversity of [email protected]

MS47

An L1 Regularization Algorithm for Reconstruct-ing Piecewise Smooth Functions from Fourier DataUsing Wavelet Projection

Several important applications use Fourier sampling. Of-ten it is advantageous to reduce samples counts. Regular-izations seeking piecewise smooth solutions are popular incompressed sensing. Total Variation denoising is a success-ful technique; but it suffers from so called staircase artifactsthat can be removed with Generalized Total Variation. Weoffer an alternative using a polynomial annihilation edgedetector and a Wavelet basis. This has a simple, robustimplementation.

Dennis DenkerArizona State University

110 IS16 Abstracts

[email protected]

MS47

Sar Moving Target Imaging in Complex Scenes Us-ing Sparse and Low-Rank Decomposition

We present a method to image complex scenes with spot-light mode SAR with the presence of moving targets. Re-cent methods that use sparsity-based reconstruction cou-pled with phase error corrections of moving targets cannothandle realistic scenarios because they assume the scene it-self is sparse. Our method makes use of the sparse and low-rank (SLR) matrix decomposition. We demonstrate withthe GOTCHA Volumetric SAR dataset that SLR can ac-curately image multiple moving targets in complex scenes.

Kang-Yu Ni, Shankar RaoHRL [email protected], [email protected]

MS47

Sar Imaging using Special Regularization Methods

Synthetic Aperture Radar (SAR) imaging is a techniqueused to construct usually 2-D approximations of a sceneby detecting scattered waves off of the scene. These scat-tered wave measurements take the form of high frequencyFourier coefficients. In this talk we present �1 regulariza-tion approaches for SAR image formation.

Toby Sanders, Rodrigo B. Platte, Anne GelbArizona State [email protected], [email protected], [email protected]

MS47

Image Reconstruction from Non-Uniform FourierData

Nonuniform Fourier data are routinely collected in applica-tions such as magnetic resonance imaging, synthetic aper-ture radar, and synthetic imaging in radio astronomy. Wewill discuss in this talk the image reconstruction from itsfinite non-uniform Fourier samples. Specifically, we pro-vide a mathematical foundation of this problem throughFourier frames and admissible frames. As a result, a stableand efficient algorithm based on that will also be presented.

Guohui SongClarkson [email protected]

MS48

Accelerating Optical Projection Tomography UsingCompressed Sensing


Simon ArridgeUniversity College [email protected]

MS48

Limited Angle Tomography and Discretization ofContinuous Inverse Problems

We consider the question how inverse problems posed for

continuous objects, for instance for continuous functions,can be discretized. This means the approximation of theproblem by finite dimensional inverse problems. We willconsider a linear inverse problem m = Au + ε. Here func-tion m is the measurement, A is an ill-conditioned linearoperator, e.g. operator modeling the limited angle X-rayimaging, u is an unknown function, and ε is random noise.The inverse problem means determination of u when m isgiven. The traditional solutions for the problem includethe generalized Tikhonov regularization and the estima-tion of u using Bayesian methods. To solve the problemin practice u and m are discretized, that is, approximatedby vectors in a finite dimensional vector space. We showpositive results when this approximation can successfullybe done in the context of Tikhonov regularization and ofthe Bayesian analysis. Also, we show problems that cansurprisingly appear in these methods. As a particular ex-ample, we consider the total variation (TV) regularizationand the Bayesian analysis based on total variation priorand the Besov priors. Also, we consider the effects causedby the fact that the Gaussian white noise, considered as afunction on an interval or a square, is not L2-valued func-tion but a generalized function (i.e., a distribution).

Matti LassasUniversity of [email protected]

MS48

Tomographic Reconstruction Using AdaptiveMcmc in Terms of Parametric Curves

The inverse problem of reconstructing of 2D shape of ahomogeneous phantom using Adaptive MCMC in term ofNon-Uniform Rational B-Splines (NURBS) is presented.The proposed method assesses the boundary shape of thephantom by estimating the control points in NURBS curveout of sparse tomography measurements. The attenuationparameter of the inside material, in this case sugar crys-tal, is recovered as well. The computations result is quitepromising, though it has a heavy computation.

Zenith PurishaUniversity of [email protected]

MS48

Computed Tomography from Limited Data Usinga Robust and Automated Discrete Algebraic Re-construction Technique

Obtaining accurate reconstruction from limited projectiondata is of high importance in tomography applications.Discrete tomography achieves this goal by incorporatingprior knowledge of the scanned object in terms of its lim-ited number of material compositions. In this work, we pro-pose a robust discrete algebraic reconstruction technique,TVR-DART, which imposes both soft discrete priors andsparsity constraints. Both numerical and experimental re-sults show that the proposed algorithm performs accuratereconstructions under practical limited data conditions.

Xiaodong ZhugeCentrum Wiskunde & Informaticathe [email protected]

Joost Batenburg

IS16 Abstracts 111

Centrum Wiskunde en [email protected]

MS49

Dose Fractionated Cryo-EM Images: Advances andFundamental Limits in Movie Alignment

The introduction of direct electron detectors in cryo-electron microscopy (cryo-EM) has had transformative ef-fects in the field. These detectors provide the capabilityof acquiring time-resolved data in movie-mode allowing forcorrection of stage and beam induced motion which are im-portant resolution limiting factors. In this talk, we presentrecent advances in motion correction of cryo-EM images aswell as fundamental limits in more general multi-image reg-istration that reveal the conditions under which alignmentis possible.

Cecilia AguerrebereDuke [email protected]

Alberto BartesaghiNCI / [email protected]

Sriram [email protected]

Guillermo SapiroDuke [email protected]

MS49

Denoising and Covariance Estimation of SingleParticle Cryo-EM Images

The problem of image restoration in cryo-EM entails cor-recting for the effects of the Contrast Transfer Function(CTF) and noise. Popular methods for image restorationinclude ‘phase flipping’, which corrects only for the Fourierphases but not amplitudes, and Wiener filtering, which re-quires the spectral signal to noise ratio. We propose anew image restoration method which we call ‘CovarianceWiener Filtering’ (CWF). In CWF, the covariance matrixof the projection images is used within the classical Wienerfiltering framework for solving the image restoration de-convolution problem. Our estimation procedure for thecovariance matrix is new and successfully corrects for theCTF. We demonstrate the efficacy of CWF by applying itto restore both simulated and experimental cryo-EM im-ages. Results with experimental datasets demonstrate thatCWF provides a good way to evaluate the particle imagesand to see what the dataset contains even without 2D clas-sification and averaging.

Tejal BhamrePrinceton [email protected]

Teng ZhangUniversity of Central [email protected]

Amit SingerPrinceton University

[email protected]

MS49

Symmetry Detection by Auto-Correlation Kernels

We consider the problem of identifying the type of spa-cial symmetry group of a biological molecule from itsnoisy cryo-EM projections from unknown viewing direc-tions. Our approach is to estimate the auto-correlation ker-nel functions of the projections and to compute the spectraof the kernels, following Kam’s theory in 1980s. Accordingto a classical theorem of Klein, the “ranks” of the auto-correlation kernels encode the type of the symmetry thatthe molecule has. We test the algorithm on synthetic andreal-world data sets.

Xiuyuan ChengYale [email protected]


Yoel ShkolniskyTel Aviv [email protected]

MS49

Angular Reconstitution for Molecules with C4 Sym-metry

We present an algorithm for determining the three-dimensional structure of molecules that have a 4-way rota-tional symmetry. Our algorithm is based on self-common-lines which induce identical lines within the same image.We show that the location of self-common-lines is relatedto the underlying image’s viewing-direction tilt angle, andthat it admits quite a few favorable geometrical constraints,thus enabling a high detection rate even in a noisy setting.

Gabi Pragier, Yoel ShkolniskyTel Aviv [email protected], [email protected]

MS50

Emerging Applications for Radar Intelligence,Surveillance, and Reconnaissance

From the first experiments in the late 19th century totoday, radar has continually evolved and become an in-dispensable tool in the area of Intelligence, Surveillance,and Reconnaissance (ISR). Todays applications includemilitary, intelligence, homeland security, resource manage-ment, and scientific missions. As new needs arise, radar of-fers the possibility of further evolution to meet those needs.We discuss in this presentation some of the emerging appli-cations for ISR to which radar imaging might offer utility.

Armin W. DoerrySandia National Laboratories

112 IS16 Abstracts

[email protected]

MS50

Electromagnetic Time Reversal

We apply the Time Reversal algorithm in a multiple-scattering environment to discover resonances for a col-lection of scatterers.

Jerry KimNaval Research [email protected]

MS50

A Functional Analytic Approach to Sar Image Re-construction

In this work we draw the connection between backprojec-tion reconstruction and best linear unbiased estimation insynthetic aperture radar imaging. It is found that in theideal imaging scenario, i.e. unlimited bandwidth and aper-ture, the backprojected image and the best linear unbiasedestimate are identical when using a microlocal criterion fordetermining the backprojection filter. From this analysis areproducing kernel criterion is derived for the ideal back-projection filter in a more general sense. We also attemptto determine the ideal Hilbert space which contains thereflectivity function in SAR imaging.

Kaitlyn Voccola MullerColorado State [email protected]

MS50

Design Considerations for Multistatic Radar Imag-ing

This talk describes design considerstions for multistaticradar imaging including geometry and pulse repetition fre-quencies for the system.

Tegan WebsterNaval Research [email protected]

MS51

The Difference of L1 and L2 for Compressive Sens-ing and Image Processing

A fundamental problem in compressed sensing (CS) is toreconstruct a sparse signal under a few linear measure-ments far less than the physical dimension of the signal.Currently, CS favors incoherent systems, in which any twomeasurements are as little correlated as possible. In reality,however, many problems are coherent, in which case con-ventional methods, such as L1 minimization, do not workwell. In this talk, I will present a novel non-convex ap-proach, which is to minimize the difference of L1 and L2

norms (L1−2) in order to promote sparsity. Efficient mini-mization algorithms will be discussed, including differenceof convex function methodology and a proximal operatorfor L1−2.

Yifei Lou, Yifei LouDepartment of Mathematical SciencesUniversity of Texas at [email protected], [email protected]

Penghang YinDepartment of Mathematics University of California,[email protected]

Jack XinDepartment of [email protected]

MS51

Majorization-Minimization for Nonconvex Opti-mization

We propose an efficient optimization algorithm based ona majorization-minimization (MM) strategy for the solu-tion of nonsmooth nonconvex minimization problems. TheMM algorithms are based on the principle of successivelyminimizing upper bounds of the objective function. Eachupper bound, or surrogate function, is locally tight at thecurrent estimate, and each minimization step decreases thevalue of the objective functional. Analysis of convergenceof the proposed approach are provided. Our experimentsshow that our method is competitive with the state of theart for the solution of nonconvex minimization problem.

Serena MorigiDepartment of MathematicsUniversity of Bologna, [email protected]

Alessandro LanzaDept.Mathematics, Univ. Bologna, [email protected]

Fiorella SgallariUniversity of BolognaDepartment of [email protected]

MS51

Algorithms for Minimizing Differences of ConvexFunctions and Applications

Several optimization schemes have been known for convexoptimization problems. However, numerical algorithms forsolving nonconvex optimization problems are still under-developed. A progress to go beyond convexity was madeby considering the class of functions representable as differ-ences of convex functions. In this talk we present a numberof algorithms for minimizing differences of convex func-tions. Then we introduce some applications of these algo-rithms to solve problems of facility location and clustering.

Mau Nam NguyenFariborz Maseeh Department of Mathematics andStatisticsPortland State [email protected]

MS51

Nonconvex Sorted L1 Minimization for Sparse Ap-proximation

In this paper, we consider a weighted �1 penalty with theset of the weights fixed and the weights are assigned basedon the sorting of all the components in magnitude. The

IS16 Abstracts 113

smallest weight is assigned to the largest component inmagnitude. This new penalty is called nonconvex sorted�1. Then we propose two methods for solving nonconvexsorted �1 minimization problems: iteratively reweighted �1minimization and iterative sorted thresholding, and provethat both methods will converge to a local minimizer ofthe nonconvex sorted �1 minimization problems. We alsoshow that both methods are generalizations of iterativesupport detection and iterative hard thresholding, respec-tively. The numerical experiments demonstrate the betterperformance of assigning weights by sort compared to as-signing by value.

Xiaolin [email protected]

Lei ShiFudan [email protected]


MS52

Automated Target Detection from CompressiveMeasurements

A novel compressive imaging model is proposed that mul-tiplexes segments of the field of view onto an infrared focalplane array. Similar to compound imaging, our model isbased on combining pixels from a surface comprising of dif-ferent parts of the FOV. We formalize this superposition ofpixels in a global multiplexing process reducing the numberof detectors required of the FPA. We then apply automatedtarget detection algorithms directed on the measurementsof this model in a scene. Based on quadratic correlation fil-ters, we extend the target training and detection processesdirectly using these encoded measurements. Preliminaryresults are promising.

Robert R. MuiseLockheed [email protected]

MS52

An Automated Design Scheme for Improved PointSpread Function Engineering


Colin OlsonNaval Research LaboratoryOptical Sciences [email protected]

MS52

Compressive Sensing of Very High-DimensionalImages and Videos


Aswin SankaranarayananCMU

[email protected]

MS52

Through-the-Wall Radar Imaging Using DiscreteProlate Spheroidal Sequences

A challenge when detecting stationary targets throughwalls is to locate the targets in the presence of wall EM re-flections, which are relatively strong compared to behind-the-wall target return. Given limited measurements of astepped-frequency radar signal, we discuss techniques formitigating wall return and detecting stationary targets byusing Modulated Discrete Prolate Spheroidal Sequences(DPSSs), a time-frequency analysis tool that offers an effi-cient basis for representing sampled bandpass signals.

Michael B. Wakin, Zhihui ZhuDept. of Electrical Engineering and Computer ScienceColorado School of [email protected], [email protected]

MS53

Fast Scattered Data Interpolation

The problem of interpolating irregularly spaced multidi-mensional data to a regular grid plays an important rolein geophysical imaging. I describe a fast O(N) algorithmfor solving this problem, where N is the size of the outputgrid. The algorithm is analogous to the method of natu-ral neighbor interpolation and is based on computing thedistance function and the distance gradient by solving theeikonal equation.

Sergey FomelUniversity of Texas at [email protected]

MS53

Babich’s Expansion and the Fast Huygens Sweep-ing Method for the Helmholtz Wave Equation atHigh Frequencies

Starting from Babich’s expansion, we develop a new high-order asymptotic method, which we dub the fast Huygenssweeping method, for solving point-source Helmholtz equa-tions in inhomogeneous media in the high-frequency regimeand in the presence of caustics. The new method enjoysthe following desired features. First, it precomputes theasymptotics in Babich’s expansion, such as traveltime andamplitudes. Second, it takes care of caustics automatically.Third, it can compute the point-source Helmholtz solutionfor many different sources at many frequencies simultane-ously. Fourth, for a specified number of points per wave-length, it can construct the wavefield in nearly optimalcomplexity in terms of the total number of mesh points,where the prefactor of the complexity only depends on thespecified accuracy and is independent of frequency. Bothtwo-dimensional and three-dimensional numerical experi-ments have been carried out to illustrate the performance,efficiency, and accuracy of the method.

Jianliang QianDepartment of MathematicsMichigan State [email protected]

Robert BurridgeDepartment of Mathematics and Statistics

114 IS16 Abstracts

University of New [email protected]

Wangtao LuMichigan State [email protected]

MS53

Affine invariant geodesics and their applications

Natural objects can be subject to various transformationsyet still preserve properties that we refer to as invariants.Here, we use definitions of affine-invariant arc-length in or-der to extend the set of existing non-rigid shape analysistools. We show that by re-defining the surface metric asits equi-affine version, the surface with its modified met-ric tensor can be treated as a canonical Euclidean objecton which most classical Euclidean processing and analy-sis tools can be applied. The new definition of a metricis used to extend the fast marching method technique forcomputing geodesic distances on surfaces, where now, thedistances are defined with respect to an affine-invariant ar-clength.


Michael Bronstein, Alex BronsteinDepartment of Computer ScienceTechnion - Israel Institute of [email protected], [email protected]

Ron KimmelTechnion, Haifa, [email protected]

Nir SochenDepartment of Applied MathematicsTel Aviv University, [email protected]

MS53

Joint Fwi and Traveltime Tomography

The full waveform inversion (FWI) is a non-linear opti-mization problem, which is solved by iterative methods likeGauss Newton. Using such methods, the resulting solutionis highly sensitive to the existence of low-frequency data,which is hard to collect. Therefore FWI is often initializedby traveltime tomography, which is achieved by solving theinverse Eikonal equation. In this talk we extend this ap-proach and jointly apply FWI and traveltime tomographyto strengthen the influence of the low-frequencies obtainedfrom the latter on the minimization process. Synthetic ex-amples show that this strategy leads to a better recovery ofthe underlying medium when low-frequency data is miss-ing.

Eran TreisterTechnion - Israel Institute of Technology, [email protected]

Eldad HaberUniversity of British Columbia

[email protected]

MS54

Learning Matrix-Valued Kernels for Shape Classi-fication in the Large Deformation Framework


Joan GlaunesUniversite Paris [email protected]

MS54

Matrix-Valued Kernels for Shape DeformationAnalysis


Mario MicheliBowdoin [email protected]

MS54

Statistical Shape Analysis Heavy Weight and LightWeight Approaches

Generating concise, accurate, robust descriptors of shaperemains an important problem in image analysis. Whilemany conventional methods for shape analysis have reliedon a relatively small set of shape descriptors, recently tech-nologies have been proposed that work directly on shapespaces, with metrics that account for the high-dimensionalproperties of shapes and the associated invariants. Suchshape metrics introduce associated heavy-weight problemsof either finding geodesics on a shape manifold or find-ing a dense set of correspondence points. Recently, re-searchers have discovered that analysis of a population ofshapes helps in the tractable computation of correspon-dences and associated metrics. In this talk we discuss re-cent work on automatic generation of correspondences andshape transformtions using populations of shapes, as wellas population-based methods that forgo transformationsall together.

Ross WhitakerSchool Of ComputingUniversity of [email protected]

MS54

Atrophy-Constrained Longitudinal Registration ofShapes Extracted from Brain Images

Diffeomorphic registration using optimal control on the dif-feomorphism group and on shape spaces has become widelyused since the development of the Large Deformation Dif-feomorphic Metric Mapping (LDDMM) algorithm. Morerecently, a series of algorithms involving sub-riemannianconstraints have been introduced, in which the velocityfields that control the shapes in the LDDMM frameworkare constrained in accordance with a specific deformationmodel. Here, we extend this setting by considering, in-equality constraints, in order to estimate surface deforma-tions that only allow for atrophy. We will present experi-mental results in longitudinal surfaces registration, whichexhibit an increased robustness when the constraint is im-posed, in a way which is reminiscent of unidimensional

IS16 Abstracts 115

monotonic regression.

Laurent YounesCenter for Imaging ScienceJohns Hopkins [email protected]

MS55

Explorations on Anisotropic Regularisation of Dy-namic Inverse Problems by Bilevel Optimisation

We explore anisotropic regularisation methods in the spiritof Holler & Kunisch, 2014. Based on ground truth data,we propose a bilevel optimisation strategy to compute theoptimal regularisation parameters of such a model for theapplication of video denoising. The optimisation poses achallenge in itself, as the dependency on one of the regulari-sation parameters is non-linear such that the standard exis-tence and convergence theory does not apply. Moreover, weanalyse numerical results of the proposed parameter learn-ing strategy based on three exemplary video sequences anddiscuss the impact of these results on the actual modellingof dynamic inverse problems.

Martin BenningInstitute for Computational and Applied MathematicsUniversity of [email protected]

Martin BenningDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of [email protected]



Verner VlacicDAMTP, University of [email protected]

MS55

Reconstructing Highly Accelerated Dynamic MRData Using Spatio-Temporal ICTGV Regulariza-tion

We propose a variational method for reconstructing imagesequences from accelerated dynamic magnetic resonance(MR) data. Our approach uses the infimal convolution oftotal generalized variation functionals (ICTGV) as regular-ization, which suitably combines higher-order spatial andtemporal regularity assumptions. By exploiting temporalredundancy, it yields a high reconstruction quality even inthe case of strong undersampling. This was in particularconfirmed on real data by achieving the second place in the2013 ISMRM challenge.


Martin HollerUniversity of [email protected]

MS55

Joint 4D Reconstruction and Perfusion Estimationvia Sparsity and Low-Rank

In biomedical imaging for brain perfusion and myocardialblood flow, e.g. via 4D-CT, ASL-MRI or SPECT/PET,tracer-kinetic field theory can unify among different modal-ities. However, standard models for 4D reconstruction andtracking reach their limits, mainly due to oversimplifiedspatial localization and misinterpretations of imbalancedsequences according to space-time. We present a newframework for tracking via sparsity and low-rank sequencedecomposition and its added value for joint 4D ill-posedinverse problems in those fields.


MS55

Tomographic Imaging of Moving Objects: A Space-Time Approach

The classical level set method approach for inverse prob-lems is based on modelling the unknown coefficient as abinary function: zero outside the level set and constantinside. This is achieved by composing a smooth level setfunction with the Heaviside step function. It was shownin [Kolehmainen, Lassas and Siltanen, SIAM J. Sci. Com-put. 30 (2008)] that for sparse-data X-ray tomographyit is advisable to replace the Heaviside function by x+

(which is zero for negative real arguments and identityfor non-negative arguments). The the X-ray attenuationfunction is modelled as zero outside the level set and bythe smooth level set function inside the level set. In par-ticular, that approach helps suppress the stretching arte-facts typical in limited-angle tomography. Regularizationis provided in the method by a penalty term involving thesquare norms of the derivatives of the level set functionup to order n. In the theoretical part of this report weshow that the x+-based level set method is equivalent toconstrained Tikhonov regularisation when n = 1, and thechoice n > 1 leads to a novel, nonlinear level set method.The solution in the case n¿1 is defined as a minimizer ofa nonlinear functional; we prove that there exists at leastone such minimizer. In the computational part we applythe level set method with n = 2 to dynamic tomographicdata interpreted as being measured from a space-time tar-get. The new method gives superior results compared tofiltered back-projection, constrained Tikhonov regularisa-tion, and total variation regularisation.

Samuli SiltanenUniversity of [email protected]

MS56

Gaussian Models for Texture Synthesis

I will discuss a series of work that uses Gaussian randomfields for texture synthesis. Results show that several nat-ural textures are well reproduced using a Gaussian model.

116 IS16 Abstracts

I will also describe an algorithm that summarizes a texturesample into a synthesis-oriented texton, that is, a small im-age for which the discrete spot noise simulation (summedand normalized randomly-shifted copies of the texton) ismore efficient than the classical convolution algorithm.

Bruno GalerneUniversite Paris [email protected]

MS56

Processing Textures in the Spectral Total-Variation Domain

In this talk we will outline the recently proposed spectraltotal-variation domain and explain how textures can beisolated and manipulated easily within this representation.Some theoretical aspects related to nonlinear spectral rep-resentations and nonlinear eigenvalue problems will be dis-cussed.


MS56

New Multifractal Parameters for Texture Classifi-cation Based on P-Exponents and P-Leaders

Mutifractal analysis supplies classification parameters fornatural or artificial textures (e.g. paintings). Their deriva-tion is based on the interplay between local and global reg-ularity exponents. We will explain the mathematical ideasbehind this derivation, and show the advantage of using p-wavelet leaders in this derivation. Illustration cover bothsimulations of random fields, and real-life textures. Thisis joint work with P. Abry, R. Leonarduzzi, C. Melot, S.Roux, M. E. Torres and H. Wendt

Stephane JaffardUniversite Paris-Est - Creteil [email protected]

MS56

Local Laplacian Filters: Theory and Applications

Standard image pyramids have been long considered ill-suited for edge-aware image manipulation the intuitionbeing that one needs discontinuous kernels like that of thebilateral filter for instance to model sharp edges. In thistalk, I will introduce the Local Laplacian Filters, a newclass of operators based on standard Gaussian and Lapla-cian pyramids. These filters achieve state-of-the-art resultson edge-aware applications like tone mapping and textureenhancement, thereby demonstrating that image pyramidsbased on smooth Gaussian kernels can actually accuratelyhandle edges. This is a joint work with Sam Hasinoff, JanKautz, Matthieu Aubry, and Frdo Durand.

Sylvain ParisAdobe Systems Inc.Cambridge Innovation [email protected]

MS57

Multiple Continuum Limits for Discrete Image In-

painting

In the course of their work on Coherence Transport*, Marzand Bornemann proposed a continuum limit for a classof discrete image inpainting algorithms. This limit wasuseful because was able to explain the cause of certainundesireable behaviour in existing algorithms, facilitatingthe design of new algorithms overcoming these difficulties.However, careful numerical experiments have revealed ad-ditional undesireable behaviour not explained by this limit.In this talk I will show that a second, alternative contin-uum limit exists accounting for this behaviour and whichis “closer’ to the discrete algorithm in a sense that I willmake precise. I will then show how this limit can be usedas a guide to design algorithms with further improvements.*Folkmar Bornemann and Tom Marz. Fast image inpaint-ing based on coherence transport. Journal of MathematicalImaging and Vision, 28(3):259-278, 2007.

Rob HockingUniversity of [email protected]

MS57

Directional Total Variation Regularization forImaging Problems

We introduce a reformulation of directional total variation(DTV) based on standard total variation (TV). DTV canbe a useful regularization tool for applications with direc-tional information, and we show that it has the same es-sential properties as TV. Using automated estimation ofdirection(s) in the object, we demonstrate the improve-ment of using DTV as a regularizer compared to standardTV. Numerical simulations are carried out for a practicalcomputed tomography reconstruction problem.

Rasmus D. KongskovTechnical University of [email protected]

MS57

A Relaxed Normal Two Split Method and An Ef-fective Weighted TV Algorithm for Euler’s ElasticaImage Inpainting

In this talk, we introduce two novel methods for solvingEuler’s elastica-based inpainting model. The energy func-tional of Euler’s elastica model involves high order deriva-tives and is nonsmooth and nonconvex, hence it is verycomplex to minimize. Our new methods are based on thetwo powerful algorithm ideas: operator splitting and al-ternating direction method of multipliers. We relax thenormal vector in the curvature term and we propose a Re-laxed Normal Two Split (RN2Split) method. In theory, weshow that the limit point of a converging sequence satisfiesthe Karush–Kuhn–Tucker conditions. The second methodconsiders solving the Euler’s elastica model in form of aweighted total variation. We prove the convergence undera mild assumption. We present numerical results for solv-ing several image inpainting problems, and we show thatour algorithms compare favorably with state-of-art algo-rithms.

Maryam YashtiniDepartment of MathematicsUniversity of [email protected]

IS16 Abstracts 117


MS57

Augmented Lagrangian Method for An Euler’sElastica Based Segmentation Model That Pro-motes Convex Contours

We discuss a new image segmentation model using an L1variant of Euler’s elastica as boundary regularization. Aninteresting feature of this model lies in its preference forconvex contours. To minimize the associated functional,we propose a novel augmented Lagrangian method thatemploys fewer Lagrange multipliers than those in the previ-ous works. Numerical experiments validate the efficiency ofthe algorithm and demonstrate new features of this model,including shape driven and data driven properties.

Wei ZhuMathematics, University of [email protected]

Egil BaeNorwegian Defence Research [email protected]

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway andDiv. of Math. Sciences, Nanyang Tech. [email protected]

MS58

Augmented Lagrangian Methods for ConstrainedOptimal Control Applied to Shape Registration

We have recently developed shape registration methodsthat solve optimal control problems in the diffeomorphismgroup subject to equality or inequality constraints thatare linear in the control and possibly non-linear in thestate variable. After providing examples of applicationsof the approach, which include multi-shape diffeomorphicregistration, registration with atrophy, or normal motionconstraints, we will describe our implementation, which isbased on the augmented Lagrangian method, and providetheoretical results that assess the existence of solutions tothese problems, together with the consistency of discreteapproximations.

Sylvain ArguillereJohns Hopkins [email protected]

Laurent YounesCenter for Imaging ScienceJohns Hopkins [email protected]

MS58

Advances in Lesion Quantification from PET/CTand PET/MR Scans

PET/CT and PET/MR scanners provide both structuraland functional information. They are frequently neededby clinicians for diagnosing and characterizing the diseasetype accurately. However, all diagnostic measurements re-quire precise segmentation of functional and anatomical

images, which is a challenging task due large variationsof pathologies, and difficulty in combining structural andfunctional information in the same settings. To addressthese challenges, I will present novel methods for accuratesegmentation and quantification of lesions from PET/CTand PET/MR images.

Ulas BagciUniversity of Central FloridaAssistant Professor of Computer [email protected]

MS58

A Fast Algorithm for Structured Low-Rank Ma-trix Completion with Applications to CompressedSensing MRI

A powerful new class of MRI reconstruction techniquespose recovery from undersampled k-space measurementsthrough matrix lifting. In the lifted domain, the prob-lem is to recover a structured and low-rank matrix fromits partial entries. These techniques provide superior re-construction quality and flexibility in sampling. However,this approach is computationally intensive, requiring SVDof several large dense matrix inversions per iteration. Toaddress this problem, we propose a novel, fast algorithmfor a class of structured and low-rank matrix completionproblems.

Mathews JacobElectrical and Computer EngineeringUniversity of [email protected]

MS58

Towards Robust Voxel-Wise Quantification of Per-fusion in Low SNR Dynamic Pet Imaging

We present a novel image processing pipeline for robustvoxel-wise quantification of perfusion in low SNR dynamicPET imaging. Physiologically similar voxels are clusteredtogether based on time activity curves to obtain a tightercontrol on bias (resolution) and reduce noise-induced bias.Moreover, the parameter estimation problem is split to fa-cilitate identifiability of physiologically meaningful param-eters. The proposed framework improves quantitative ac-curacy, and has long-term potential to enhance detection,staging and management of coronary artery disease.

Hassan Mohy-Ud-DinYale [email protected]

MS59

Solving Ptychography with a Convex Relaxation

Ptychography is a powerful imaging technique that trans-forms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, most al-gorithms that currently solve this reconstruction problemlack stability, robustness, and theoretical guarantees. Thistalk first presents a convex formulation of the ptychographyproblem, which has no local minima and can be solved us-ing a wide range of algorithms. It then considers a specificalgorithm, based on low-rank factorization, whose runtimeand memory usage are near-linear in the size of the out-put image. Experiments demonstrate that this approachoffers a 25% lower background variance on average thanalternating projections, the ptychographic reconstruction

118 IS16 Abstracts

algorithm that is currently in widespread use. Finally, thistalk considers an extension of this new algorithm to thereconstruction problem in 3D diffraction tomography.

Roarke HorstmeyerCalifornia Institute of [email protected]

MS59

Phase Retrieval with Missing Data

Missing data in coherent X-ray diffraction imaging arisesin experiment from, for example, the beam stop. We showhow to modify algorithms for missing data and then evalu-ate their ability to recover both the phase and missing datafrom experiments. We then discuss regularization and ad-dressing confidence in the experimental values.

Todd MunsonArgonne National LaboratoryMathematics and Computer Science [email protected]

MS59

Reconstruction Algorithms for Blind Ptycho-graphic Imaging

In scanning ptychography, an unknown specimen is illu-minated by a localised illumination function resulting inan exit-wave whose intensity is observed in the far-field.A ptychography dataset is a series of these observations,each of which is obtained by shifting the illumination func-tion to a different position relative to the specimen withneighbouring illumination regions overlapping. Given aptychographic data set, the blind ptychography problemis to simultaneously reconstruct the specimen, illumina-tion function, and relative phase of the exit-wave. Inthis talk I will discuss a nonsmooth optimisation frame-work which interprets current state-of-the-art reconstruc-tion methods in ptychography as (non-convex) alternat-ing minimization-type algorithms. Within this framework,a proof of global convergence to critical points using theKurdyka-Lojasiewicz property is provided.

Matthew TamUniversity of Goettingen, [email protected]

MS59

Survey and Benchmarking of Compressive SensingPhase Retrieval Methods

Compressive phase retrieval is a novel method for solvingthe phase problem. It exploits sparsity under some mathe-matical transformation of the quantity we wish to recover:rather than recovering the original non-sparse quantity, weapply a sparsifying transformation which ”compresses” in-formation into as few matrix elements as possible, and thenproceeds to recover this simplified representation. We com-pare standard formulations of the compressive phase re-trieval optimization problem, and perform benchmarkingtests to evaluate algorithmic effectiveness.

Ashish TripathiMathmatics and Computer Science DivisionArgonne National Laboratory

[email protected]

MS60

Reconstruction of Images from Highly Noisy andSparse Observations Using Data-driven Priors

In many image analysis problems we seek to reconstructa spatial field. In Bayesian inverse problems we need toconstruct likelihood and prior probability density func-tions. I will present a methodology that combines super-vised learning with classical Gibbs measures for likelihoodand smoothness priors to construct likelihood and priorfunctions. I will discuss the computational challenges inworking with such probability functions and will presentexperimental results for an image segmentation problem.


MS60

Optimal Experimental Design for Imaging Subsur-face Flow

Designing experiments for imaging fluid flow requires theintegration of the dynamical system describing the flow,the geophysical imaging technique, and historic data. Inthis talk we explore optimal experimental design methodsfor such problems, and demonstrate the applicability of thetechniques for the problem of imaging subsurface flow usingseismic methods.

Jennifer FohringThe University of British [email protected]

MS60

Multi-Level Accelerated Algorithm for Large-ScaleConvex Composite Minimization

We propose a multi-level algorithm for solving convex com-posite optimization problems. Our method exploits thefact that many applications that give rise to large-scaleproblems can be modelled using varying degrees of fidelity.We show that it converges to a minimizer with optimalO(1/

√ε) rate. Using numerical experiments we show that

on large-scale computer vision problems our algorithm isseveral times faster than the state of the art.

Vahan Hovhannisyan, Panos Parpas, Stefanos ZafeiriouImperial College [email protected],[email protected], [email protected]

MS60

A Multilevel Solver for the Rada-Chen SelectiveSegmentation Model and Its Extensions

In medical imaging, selective segmentation for identifica-tion of abnormalities is incredibly important. It is alsoimportant that this segmentation be achieved quickly withminimal input from the user. In this talk I will discuss afast multigrid solution for the Rada-Chen (2012) model andextensions to this model. The implementation of this al-lows very quick segmentation of user selected items withinan image. Various results will be shown and open problems

IS16 Abstracts 119

discussed.

Mike RobertsUniversity of Liverpool)[email protected]


Klaus IrionRoyal Liverpool and Broadgreen University HospitalsNHS [email protected]

MS61

Nonconvex Regularization and Satellite Imagery

There are several benefits to regularizing the processing ofimages with nonconvex penalty functions, such as the �p

norm with p < 1. Examples in the literature include pre-serving the shape of edges when denoising images, recoveryof sparse images from fewer measurements, and better ex-traction of moving objects from video. In this talk, wewill look at examples drawn from recent work at DescartesLabs, a company that processes huge amounts of satelliteimagery to extract useful information.

Rick ChartrandLos Alamos National [email protected]

MS61

Reconstruction of Sparse Images with Emitter-Based Posterior Mean Estimates

Solving inverse problems with maximum a posteriori ap-proaches often produces reconstruction artifacts in images.A well-known example is the so-called night sky effect, ob-served when the reconstructed image is constrained to benon-negative. We show that this artifact can be avoided byconsidering the posterior mean, estimated with an MCMCalgorithm. To reconstruct sparse images, a non-convexmodel based on emitters can be used with a similar al-gorithm. Its usefulness is illustrated for super-resolutionmicroscopy.

Lionel MoisanParis [email protected]

Anne-Sophie MaceBioaxial and Universite Paris [email protected]

Julien [email protected]

MS61

Smoothness and Sparsity Enhanced Electroen-cephalogram Brain Image Reconstruction

Electroencephalography (EEG) is a non-invasive techniquethat reconstructs functional brain images by measuringscalp electrical potentials. In this work, we propose aSparsity and Smoothness enhanced Method Of Optimized

electrical TomograpHy (s-SMOOTH) to improve the re-construction resolution and quality. Specifically, the To-tal Generalized Variation (TGV) defined on a triangularmesh is proposed to enhance high-order smoothness ofEEG brain image, and the �1−2 regularization is utilizedto reduce localization error. A large variety of experimentson synthetic data with different source configurations andnoise levels demonstrate the advantages of our method interms of total reconstruction accuracy, localization accu-racy and focalization degree. The tests on event-relatedpotential data from normal subject further demonstratethe outstanding performance of the proposed method inpractice.

Ying LiDepartment of BioengineeringUniversity of California, Los [email protected]

Jing Qin, Jing QinUniversity of California Los [email protected], [email protected]


Wentai LiuDepartment of BioengineeringUniversity of California, Los [email protected]

MS61

Transformed Schatten-1 Iterative Thresholding Al-gorithms for Matrix Rank Minimization

We study a non-convex low-rank promoting penalty func-tion, the transformed Schatten-1 (TS1), and its applica-tions in matrix completion. The TS1 penalty, as a matrixquasi-norm defined on its singular values, interpolates therank and the nuclear norm through a nonnegative param-eter a ∈ (0,+∞). We consider the unconstrained TS1regularized low-rank matrix recovery problem and developa fixed point representation for its global minimizer. TheTS1 thresholding functions are in closed analytical formfor all parameter values. The TS1 threshold values differ insubcritical (supercritical) parameter regime where the TS1threshold functions are continuous (discontinuous). Wepropose TS1 iterative thresholding algorithms and comparethem with some state-of-the-art algorithms on matrix com-pletion test problems. For problems with known rank, afully adaptive TS1 iterative thresholding algorithm consis-tently performs the best under different conditions, whereground truth matrices are generated by multivariate Gaus-sian with varying covariance. For problems with unknownrank, TS1 algorithms with an additional rank estimationprocedure approach the level of IRucL-q which is an itera-tive reweighted algorithm, non-convex in nature and bestin performance.

Shuai ZhangDepartment of MathematicsUniversity of California, [email protected]

Jack XinDepartment of MathematicsUCI

120 IS16 Abstracts

[email protected]

Penghang YinDepartment of Mathematics University of California,[email protected]

MS62

Scalable Information Optimal Imaging: RecentProgress - EO/IR to X-Ray


Amit AshokCollege of Optical SciencesThe University of [email protected]

MS62

Lensfree Imaging

We present a thin form-factor lensless camera, FlatCam,that consists of a coded mask placed on top of a bare, con-ventional sensor array. FlatCam is an instance of a codedaperture imaging system in which each pixel records a lin-ear combination of light from multiple scene elements. Acomputational algorithm is then used to demultiplex therecorded measurements and reconstruct an image of thescene. In contrast with vast majority of coded aperturesystems, we place the coded mask extremely close to theimage sensor that can enable a thin system. We use a sep-arable mask to ensure that both calibration and image re-construction are scalable in terms of memory requirementsand computational complexity. We demonstrate the po-tential of our design using a prototype camera built usingcommercially available sensor and mask.

Richard G. BaraniukRice UniversityElectrical and Computer Engineering [email protected]

Salman Asif, Ali AyremlouRice [email protected], [email protected]

Aswin [email protected]

Ashok VeeraraghavanRice [email protected]

MS62

Fast Reconstruction Methods forSpatiotemporally-Encoded MRI

This work examines image reconstruction tasks arising inmagnetic resonance imaging (MRI) applications that arecharacterized by the use of a novel class of spatiotemporal(non-Fourier) acquisition sequences. We describe how theunique structure inherent to these imaging sequences maybe leveraged and exploited in the reconstruction approach,yielding a flexible and computationally-efficient suite of re-construction methods for these problems. Experimentalevaluations demonstrate the efficacy of our approach for

this novel imaging modality.

Alex Gutierrez, Di Xiao, Jarvis Haupt, Albert Jang,Michael GarwoodUniversity of [email protected], [email protected], [email protected],[email protected], [email protected]

Steen MoellerUniversity of MinnesotaCenter for Magnetic Resonance [email protected]

MS62

Progress on Developing a Computational ImagerUsing Integrated Photonics

We will describe the development of a thin form-factor im-ager based on interferometric imaging and integrated pho-tonics. The system is designed to measure specific compo-nents of the Fourier transform of the 2D intensity distribu-tion of a scene. An image reconstruction algorithm is thenused to create actual images. System design and recon-struction options will be discussed in detail. Results froman initial proof-of-concept experiment will be presented.

Samuel ThurmanLockheed Martin Space Systems Companyn/a

Alan Duncan, Richard Kendrick, Chad Ogden, DanielleWuchenichLockheed Martin Advanced Technology [email protected], [email protected],[email protected], [email protected]

Tiehui Su, Shibnath Pathak, Wei-Cheng Lai, MathiasProst, Roberto Proietti, Ryan Scott, S.J.B. YooUniversity of California [email protected], [email protected],[email protected], [email protected],[email protected], [email protected],[email protected]

MS63

Incorporating a Spatial Prior into Nonlinear D-BarEit Imaging for Complex Admittivities

Electrical Impedance Tomography imaging aims to recoverthe internal conductivity and permittivity distributionsfrom electrical measurements taken at the surface of an ob-ject. The reconstruction task is a severely ill-posed nonlin-ear inverse problem that is highly sensitive to measurementnoise and modeling errors. D-bar methods have showngreat promise in producing noise-robust implementable al-gorithms by employing a low-pass filter in a nonlinearFourier domain. Unfortunately, the low-pass filtering canlead to a loss of sharp edges in the reconstruction. Re-cently, [Alsaker and Mueller, “A D-bar Algorithm with apriori Information for 2-D Electrical Impedance Tomogra-phy’, 2015] showed that incorporating spatial prior data,e.g. in the form of a CT scan that includes the approxi-mate locations of major features such as the heart, lungs,spine etc., can greatly improve the spatial sharpness of aconductivity image by increasing the radius of the filter inthe nonlinear Fourier domain. In this talk, the approachis extended to admittivity (conductivity as well as permit-tivity) EIT imaging. Noise-robust reconstructions are pre-sented for simulated EIT data on chest-shaped phantoms

IS16 Abstracts 121

extracted from CT scans.

Sarah HamiltonMarquette [email protected]

Jennifer L. MuellerColorado State UniversityDept of [email protected]

Melody AlsakerColorado State [email protected]

MS63

Direct Inversion from Partial Boundary Measure-ments by Data Extrapolation

In electrical impedance tomography, the assumption of fullboundary data is not always practical. In this context weintroduce the partial boundary inverse conductivity prob-lem in a realistic setting and analyze the error that partialboundary measurements introduce. Additionally we pro-pose an extrapolation approach of the measured data. Forreconstructing the conductivity we apply a Born approx-imation. Computational convergence results and recon-structions are presented for medical motivated simulateddata.

Andreas HauptmannUniversity of [email protected]

MS63

Optimal Ultrasound Frequency for Lung Moni-toring Through Ultrasound Informed ElectricalImpedance Tomography: Numerical Simulations

Electrical Impedance Tomography images of the lung im-prove when anatomical and physiological prior informa-tion is available. Ultrasound Tomographic images can bea source of prior information for EIT inverse problems.Higher frequencies reflect at the pleura and are quickly ab-sorved in the lung tissue. Lower ultrasound frequenciesworsens the spatial resolution of ultrasound tomographicimages. The present work investigates the optimal fre-quency for spatial resolution and penetration of ultrasoundin the lung tissue.

Raul G. LimaUniversity of Sao [email protected]

MS63

Edge detection in Electrical Impedance Tomogra-phy

In this talk we will present a new imaging method able toreconstruct discontinuities (e.g. edges of inclusions) of anelectrical conductivity from boundary voltage and currentmeasurements. The method combines the high contrastsensitivity of Electrical Impedance Tomography with im-proved spatial resolution obtained through introduction ofa nonphysical (virtual) variable. This talk presents thetheoretical background of the method as well as numericalreconstructions. This is a joint work with A. Greenleaf, M.

Lassas, S. Siltanen and G. Uhlmann.

Matteo SantacesariaPolitecnico di [email protected]

MS64

Metamorphoses of Functional Shapes in SobolevSpaces

We describe in detail a joint model of geometric-functionalvariability between signals defined on deformable mani-folds. These objects called fshapes were first introducedin [Charon et al. 2015]. Building on this work, we ex-tend the original L2 model to treat signals of higher reg-ularity on their geometrical support with stronger Hilbertnorms (typically Sobolev). We describe the Hilbert bun-dle structure of such spaces and construct metrics basedon metamorphoses, that groups into one common frame-work both shape deformation metrics and usual (flat) im-age metamorphoses. We then propose a formulation ofmatching between any two fshapes from the optimal con-trol perspective, study existence of optimal controls andderive Hamiltonian equations describing the dynamics ofsolutions. Secondly, we tackle the discrete counterpart ofthese problems and equations as well as the important issueof Γ-convergence of discrete solutions to continuous ones.At last, we show a few results of this fshape metamorpho-sis approach for the classification of retinal tissues withthickness measurements.

Nicolas CharonCenter for Imaging SciencesJohns Hopkins [email protected]

MS64

A Fast Iterative Algorithm to Compute ElasticShape Distance Between Curves

We propose a fast iterative algorithm to compute an elas-tic shape distance between two closed curves. The shapedistance is based on the square-root velocity functions pro-posed by Srivastava et al (PAMI,2011), and is invariant toscaling, translation, and rotation. We pose the distancecomputation as an energy minimization problem, where wecompute the optimal seed, rotation, and diffeomorphism.We develop alternating iterations, using fast dynamic pro-gramming and nonlinear optimization for the diffeomor-phism, and FFT for the seed and the rotation. Our algo-rithm results in subquadratic running times with respectthe number of nodes of the curves.

Gunay DoganTheiss Research, [email protected]

Javier Bernal, Charles HagwoodNational Institure of Standards and [email protected], [email protected]

MS64

Irrotational Diffeomorphisms for Image Registra-tion and Density Matching


Sarang Joshi

122 IS16 Abstracts

Scientific Computing and Imaging InstituteUniversity of [email protected]

MS64

Scale Invariant Metrics of Volumetric Datasets

Nature reveals itself in similar structures of different scales.A child and an adult share similar organs yet dramaticallydiffer in size. Comparing the two is a challenging task toa computerized approach as scale and shape are coupled.Here we show that a local measure based on the Scalarcurvature can be used to normalize the local metric of thestructure and then used to extract global features and dis-tances. This approach is relevant for any dimension, andis extremely useful for 3-manifolds, such as Computed To-mography (CT) and Magnetic Resonance Imaging (MRI).


Ramesh RaskarMassachusetts Institute of [email protected]

MS65

A Non-Local Bayesian Method for Video Denoising

Advances in video sensor hardware have steadily improvedthe acquisition quality. However, video cameras are beingused more each time, and in less favorable situations, re-sulting in high levels of noise. We present a new Bayesianpatch-based video denoising method using 3D rectangularpatches and not requiring motion estimation. The methodcompares favourably to the state-of-the-art, both in termsof PSNR and temporal consistency attained.

Pablo AriasENS [email protected]

Jean Michel MorelCMLA (CNRS UMR 8536)ENS Cachan (France)[email protected]

MS65

Pewa: Patch-Based Exponentially Weighted Ag-gregation for Image Denoising.

We present a statistical aggregation method, which com-bines image patches denoised with conventional algorithms.We evaluate the SURE estimator of each denoised can-didate image patch to compute the exponential weightedaggregation (EWA) estimator. The PEWA algorithm hasan interpretation with Gibbs distribution, is based on aMCMC sampling and is able to produce results that arecomparable to the current state-of-the-art. C. Kervrann.PEWA: Patch-based Exponentially Weighted Aggregationfor image denoising. NIPS’14, Montreal, Canada, 2014.

Charles KervrannInriaRennes, France

[email protected]

MS65

Boosting of Image Denoising Algorithms

A generic recursive algorithm for improving denoising al-gorithms is proposed. Given the initial denoised image,we suggest repeating the following ’SOS’ procedure: (i)Strengthen the signal by adding the previous denoised im-age to the degraded input image, (ii) Operate the denoiseron the strengthened image, and (iii) Subtract the previousdenoised image from the restored signal-strengthened out-come. The convergence of this process is studied, showingthat the SOS acts as a graph Laplacian regularizer

Yaniv [email protected]


MS65

Towards Bias Reduction in Image Denoising Algo-rithms

Bias in image restoration can hamper further analysis, typ-ically when the pixel intensities have a physical meaning.During this talk, we address the problem of modeling thedifferent sources of bias arising in classical restoration tech-niques. Based on this study, we develop bias reductiontechniques that apply to a large class of estimators, in-cluding recent variational and patch-based methods. Wefinally discuss the performance and relevance of reducingbias according to the focused applications.

Charles-Alban Deledalle, Charles-Alban DeledalleCNRS, IMB, Universite [email protected],[email protected]

Nicolas PapadakisCNRS/[email protected]

Joseph SalmonTelecom-ParisTech, CNRS [email protected]

Samuel VaiterCNRS, IMB, Universite de [email protected]

MS66

Title Not Available


Anna MichalakCarnegie Institution for Science and Stanford University,[email protected]

MS66

Computational Approaches for Massive Multi-

IS16 Abstracts 123

Frame Blind Deconvolution

In this talk we consider multi-frame blind deconvolution(MFBD). There are many optimization approaches thatcan be applied to these problems, but they are generallylimited in the number of frames that can be processed. Inthis talk we consider efficient computational approaches toreduce a massive number of data frames to a computation-ally manageable set, while still preserving all informationfor MFBD algorithms.


MS66

Local Solver for Seismic Full Waveform Inversion

In certain seismic problems, updates to the velocity modeloften have a highly localized nature. Numerical techniquessuch as full waveform inversion (FWI) require an estimateof the wavefield to compute the model updates. Whendealing with localized problems it is wasteful to computethese updates in the global domain, when we only needthem in our region of interest. Here we introduce a solverfor efficiently generating the local wavefields required forlocal updates.

Bram [email protected]

Alison MalcolmMemorial University of [email protected]

MS66

Reduced-Order Models in Large-Scale SeismicImaging

We developed a novel inversion approach based on the the-ory of projection-based model reduction. We construct adata-driven reduced-order model from the data sampledat the rate close to the Nyquist limit. The system corre-sponds to the full-scale system projected onto the subspaceof orthogonalized time-domain solution snapshots. This or-thogonalization removes the dominant part of all the mul-tiples, and, consequently, avoids one of the key challengesin seismic inversion. Numerical examples will finalize thetalk.

Mikhail Zaslavsky, Vladimir L. DruskinSchlumberger-Doll [email protected], [email protected]

Alexander V. MamonovUniversity of [email protected]

MS67

On the Choice of Loss Functions and Their Esti-mations for Relevant Parameter Selection in ImageRestoration

The Stein unbiased risk estimator provides an estimate ofthe square error in image restoration problems subject toGaussian noise. It can be used as an objective for param-

eter selection. This square error estimator has been ex-tended beyond Gaussian perturbations. However, in suchcases, we will show that optimizing the square error canlead to selecting irrelevant parameters. In this talk, weconsider more appropriate loss functions and discuss thechallenging problem of estimating them.

Charles-Alban Deledalle, Charles-Alban DeledalleCNRS, IMB, Universite [email protected], [email protected]

MS67

Automatic Parameter Selection for Total VariationMinimization in Image Restoration

In this talk we consider functionals consisting of one or twodata-terms, a regularization-term, and parameters weight-ing the importance of the terms. Several different param-eter choice rules for functionals containing only one pa-rameter have been presented in the past, while the liter-ature is rather scarce when more than one parameter hasto been chosen. We revisit the disrcepancy principle anddemonstrate how it can be used for finding parameters infunctionals consisting of two data-terms.

Andreas LangerUniversity of StuttgartInstitute of Applied Analysis and Numerical [email protected]

MS67

Function-driven Data Learning for Image Denois-ing

Motivated by the increased demand in robust predictiveand reconstruction methods in image analysis, we presentanalysis techniques and numerical methods to explore newapplications in tractable and robust automatic learning offunctions and data structures in high dimension from theminimal number of observed samples. The performanceand robustness of the constructed algorithms are demon-strated for tractable automatic learning of optimal regu-larization parameter for image denoising procedure.

Valeriya NaumovaSimula Research [email protected]

MS67

Non-Convex Objectives: Role of the Regulariza-tion Parameter in the Local and the Global Mini-mizers

Nonconvex nonsmooth objectives, composed of a data termand a regularization term weighted by a parameter, arewidely used in imaging. For a large family of such objec-tives, the merely local (not global) minimizers are inde-pendent of this parameter. All algorithms converging toonly local minimizers need a careful choice of the parame-ter even though the solution thus found is independent ofit. Our talk gives insights into this visible contradiction.

Mila NikolovaCentre de Mathematiques et de Leurs Applications(CMLA)ENS de Cachan, CNRS, PRES UniverSud

124 IS16 Abstracts

[email protected]

MS68

Statistical Modeling of Fmri Data for Pre-SurgicalPlanning

Spatial smoothing is essential in functional magnetic reso-nance imaging (fMRI) data analysis. In pre-surgical plan-ning, using fMRI to determine functionally eloquent re-gions of the brain image, spatial accuracy is paramount.Methods that rely on global smoothing are not reasonable,blurring boundaries between activation and non- activa-tion. Moreover, in standard fMRI analyses strict false pos-itive control is desired. For pre-surgical planning falsenegatives are of greater concern. We present two Bayesianmodels that circumvent these problems.

Timothy D. JohnsonDepartment of BiostatisticsUniversity of [email protected]

MS68

Topological Data Analysis for Functional Neu-roimaging

Topological data analysis (TDA) is a relatively new devel-opment at the intersection of mathematics, statistics, andcomputer science. The approach, which focuses on topo-logical features of a data set, is particularly suited for BigData, often characterized by complicated structure such asimages. In this talk, I will discuss the basics of TDA, em-phasizing persistent homology and its uses for functionalneuroimaging data.

Nicole LazarDepartment of StatisticsUniversity of [email protected]

MS68

Functional and Imaging Data in Precision Medicine


Todd OgdenDepartment of BiostatisticsColumbia [email protected]

MS68

Local and Global Statistical Connectomic Testing


Russell ShinoharaDepartment of Biostatistics and EpidemiologyUniversity of [email protected]

MS69

Integrated Imaging: Creating Images from theTight Integration of Algorithms, Computation, andSensors

In this talk, we present research on imaging systems thatintegrate sensor design and reconstruction algorithms for

applications in both materials and biological imaging. Theapplications include computed tomography (CT), trans-mission electron microscopy (STEM), synchrotron beamimaging, and scanning electron microscopy (SEM). In eachof these examples, the key advantages result from the use ofmodels of both the sensor and image along with the tightintegration of reconstruction algorithms with the sensingsystem design.

Charles BoumanSchool of ECEPurdue [email protected]

MS69

Multigrid-Based Optimization Approach for Multi-Modality Tomographic Reconstruction

Fluorescence tomographic reconstruction can be used to re-veal the internal elemental composition of a sample whiletransmission tomography can be used to obtain the spatialdistribution of the absorption coefficient inside the sample.In this work, we integrate both modalities and formulate anoptimization approach to simultaneously reconstruct thecomposition and absorption effect in the sample. By usingmultigrid-based optimization framework (MG/OPT), sig-nificant speedup and improvement of accuracy has shownfor several examples.

Zichao DiArgonne National [email protected]

Sven LeyfferArgonne National [email protected]

Stefan WildArgonne National [email protected]

MS69

Multi-Contrast MRI Reconstruction withStructure-Guided Total Variation

Magnetic resonance imaging is a versatile imaging tech-nique that allows to change the contrast depending on theacquisition parameters. Many clinical imaging studies ac-quire data for multiple contrasts which makes the overallscanning procedure time consuming. Having one image ofthese contrasts available, we can reconstruct the other im-ages from highly undersampled data exploiting the a priorisimilarity between the images. To achieve this goal we ex-tend total variation regularization to accommodate a prioridirectional information.

Matthias J. EhrhardtUniversity College [email protected]

Marta BetckeUniversity of College London, [email protected]

MS69

Integration of Photoacoustic and Ultrasound Com-

IS16 Abstracts 125

puted Tomography

We propose a paradigm shift in the way that imagesare reconstructed in hybrid photoacoustic/ultrasound com-puted tomography (PACT/USCT) imaging. We proposeto jointly reconstruct the absorbed optical energy densityand SOS distributions from a combined set of USCT andPACT measurements, thereby reducing the two reconstruc-tion problems into one. A non-convex optimization prob-lem is considered, which is solved by use of an alternatingalgorithm. Numerical studies reveal the numerical proper-ties of this approach.

Mark A. AnastasioDept. of Biomedical EngineeringIllinois Institute of [email protected]

Thomas MatthewsDepartment of Biomedical EngineeringWashington University in St. [email protected]

MS70

Wavelet Frame Based Piecewise Smooth ImageModel and It’s Relation to Mumford-Shah Func-tional


Jian-Feng CaiDepartment of MathematicsHong Kong University of Science and [email protected]


Zuowei ShenNational University of [email protected]

MS70

Simultaneous Tomographic Reconstruction andSegmentation with Class Priors

We consider tomographic imaging problems where the goalis to obtain both a reconstructed image and a correspond-ing segmentation. A classical approach is to first recon-struct and then segment the image. In this talk, I willintroduce a hybrid approach that simultaneously producesboth a reconstructed image and a segmentation. We incor-porate priors about the desired classes of the segmentationthrough a Hidden Markov Measure Field Model, and weimpose a regularization term for the spatial variation ofthe classes across neighboring pixels. Simulation experi-ments with artificial and real data demonstrate that ourcombined approach can produce better results than theclassical two-step approach.

Yiqiu DongTechnical University of DenmarkDepartment of Applied Mathematics and [email protected]

Per Christian HansenTechnical University of Denmark

Informatics and Mathematical [email protected]

Mikhail Romanov, Anders Bjorholm DahlTechnical University of DenmarkDTU [email protected], [email protected]

MS70

A New Multiplicative Denoising Variational Modeland its Fixed-point Proximity Algorithm

The restoration of images contaminated by Multiplicativenoise (also known as speckle noise) is a key issue in co-herent image processing. By exploring the intrinsic fea-ture embedded in images that they are often highly com-pressible under suitably chosen transforms, this paper in-troduces a variational restoration model for multiplicativenoise reduction that consists of a term reflecting the ob-served image and multiplicative noise, a quadrature termmeasuring the closeness of the underlying image in a trans-form domain to a sparse vector, and a sparse regularizer forremoving multiplicative noise. Different from the popularexisting models focusing on pursuing convexity, the pro-posed sparsity-aware model is nonconvex. We characterizethe solutions of the nonsmooth and nonconvex model viacoupled fixed-point equations that are derived from theproximity operators of the functions associated with themodel. Based on the characterization, an algorithm forfinding the critical points of the objective function of themodel is developed and convergence of the algorithm isstudied. Experimental results show that our method canremarkably outperform the state-of-art methods in termsof the quality of the restored images.

Jian LuShenzhen [email protected]

MS70

A Universal Variational Framework for SparsityBased Image Inpainting


Fang LiEast China Normal [email protected]

Tieyong ZengDepartment of MathematicsHong Kong Baptist [email protected]

MS71

A Fast-Transform-Based, High-Resolution Compu-tational Imager Using Virtual Channels

A joint sensing-reconstruction algorithm and architectureis presented that mathematically combines elements of afocal-plane array into coarse “virtual channels” represent-ing distinct regions of a field of view (FOV). In this setup,the light field from an observed scene is partitioned andencoded using patterns on a spatial light modulator, andthe light intensity of each channel is recorded. When a suf-ficient number of measurements have been obtained theyare used to computationally reconstruct an image. Beforeobserving the scene the optical system’s response function

126 IS16 Abstracts

is measured and stored as a global “point-spread function”(PSF). The reconstruction algorithm incorporates the PSFto help correct for the system’s optical aberrations, includ-ing distortions and crosstalk between channels. Further,by separating the PSF operator, which is fixed, from thesensing procedure, which is dynamic, we can efficiently im-plement image reconstruction using a fast transform as-sociated with the measurement patterns (e.g., Hadamard).The virtual channel approach offers flexibility to create dif-ferent sized (and not necessarily square) partitions of theFOV, which permits more freedom in trading different pa-rameters to achieve desired reconstruction characteristics,e.g., frame rate versus resolution.

Matthew A. HermanInview [email protected]

Tyler Weston, Lenore McMackinInView Technology [email protected],[email protected]

MS71

Convex Cardinal Shape Composition


Justin RombergSchool of ECEGeorgia [email protected]

MS71

Coherent Camera Arrays



MS71

Gigapixel Phase Imaging

This talk will describe new methods for achieving gigapixel-scale 3D intensity and phase images in a commercial mi-croscope, by computational imaging. We describe setupsemploying illumination-side and detection-side coding ofangle (Fourier) space for capturing 4D phase-space (e.g.light field) and phase retrieval datasets with fast acquisi-tion times. Experimentally, we achieve real-time 3D andphase imaging with digital aberration correction and miti-gation of scattering effects. The result is a high-resolutionimage across a large field-of-view, achieving high space-bandwith-time product. Such computational approachesto optical microscopy add significant new capabilities tocommercial microscopes without significant hardware mod-ification.

Laura [email protected]

MS72

The Use of the Approximation Error Method andBayesian Inference to Introduce Anatomical and

Physiological Prior Information into EIT Recon-struction Algorithms

Some EIT reconstruction algorithms may have their reso-lution improved using the approximation error method andBayesian inference to include prior information in the EITinverse problem. Seeking for minimal modifications to EITalgorithms, these algorithms could be extended to generatevoltages at electrodes after having generated an impedi-tivity distribution. Under these circumstances, modelingerrors are incorporated to the noise probability distribu-tion model by the application of the approximation errormethod and anatomical prior is introduced by Bayesianinversion method.

Talles Batista Rattis SantosUniversity of Sao Paulo, [email protected]

Raul Gonzalez LimaUniversity of Sao [email protected]

Erick Dario Leon Bueno de Camar, Fernando Silva deMouraThe Federal University of [email protected], [email protected]

MS72

A 3-D Analogue to the 2-D D-Bar Method

A direct 3-D D-bar reconstruction method is developedusing the low frequency limit of complex geometrical opticssolutions as proposed by Cornean et al (J Inverse and Ill-posed Problems 2006). This method varies from other 3-Dalgorithms in that it provides a 3-D analogue to the 2-DD-bar method. This algorithm was implemented for usein a rectangular prism geometry and simulated data wasgenerated for this domain. Here we present the algorithmand results of the reconstruction of the simulated data.Extensions to other geometries will also be discussed.

Peter MullerColorado State [email protected]

MS72

Convergence and Regularization for Monotonicity-Based EIT Shape Reconstruction

In electrical impedance tomography (EIT), the aim is toestimate internal electrical properties of an object by an-alyzing current and voltage data measured on its outerboundary. The idealized problem formulation is to solvefor the conductivity distribution given the correspondingNeumann-to-Dirichlet (ND) map. This problem is ill-posedand thus, in practice, only limited information about theconductivity can be recovered. Recently it was shown thata simple monotonicity property of the linearized ND mapcan be used to characterize shapes of inhomogeneities ina known background conductivity. This talk focuses on amonotonicity-based shape reconstruction scheme that ap-plies to approximative EIT measurement models, and reg-ularizes against noise and modelling error. It is demon-strated that for admissible choices of regularization pa-rameters the inhomogeneity shapes are detected, and un-der suitable assumptions, asymptotically exactly charac-

IS16 Abstracts 127

terized. The result is rigorously associated with the com-plete electrode model (CEM), and a monotonicity-basedreconstruction algorithm is formulated for the CEM. Nu-merical reconstructions from both simulated and real-worldmeasurement data are presented.

Stratos StaboulisTechnical University of [email protected]

MS72

On Uniqueness of An Inverse Problem for Time-Harmonic Maxwells Equations


Ting ZhouNortheastern [email protected]

MS73

Multiscale Extremal Points on Plane Curves, WithApplications to Shape Matching and Detection


Matt FeiszliFiftyThree, [email protected]

MS73

Parallel Transport of Distributions on TangentSpaces on Shape Spaces


Shantanu [email protected]

MS73

Multiscale Covariance Fields and Shape Character-ization in Euclidean Spaces

We introduce the notion of multiscale covariance tensorfields (CTF) associated with Euclidean random variablesas a gateway to the shape of their distributions. MultiscaleCTFs quantify variation of the data about every point inthe data landscape at all spatial scales, unlike the usual co-variance tensor that only quantifies global variation aboutthe mean. We prove stability theorems with respect to theWasserstein distance between probability measures, obtainconsistency results, as well as estimates for the rate of con-vergence of empirical CTFs.

Facundo MemoliOhio State [email protected]

MS73

Statistical Modeling of Geometries of Tree-LikeStructures

We develop a framework for shape analysis of axonal treesrepresented by (1) a main branch viewed as a parameter-ized curve in R

3, and (2) secondary branches that emanatefrom arbitrary points on the main branch. Our framework

extends the previous elastic shape analysis of Euclideancurves to the space of such trees. The space inherits a Rie-mannian metric from the spaces of individual curves, whichwe use to compute distances and geodesics.

Adam Duncan, Eric KlassenFlorida State [email protected], [email protected]

Xavier DescombesINRIA Sophia [email protected]

Anuj SrivastavaFlorida State [email protected]

MS74

Variance Stabilization for Noisy+Estimate Combi-nations in Iterative Poisson Denoising

We consider an iterative approach to progressively im-prove the effectiveness of variance-stabilizing transforma-tions (VST) adopted by Gaussian filters for denoising Pois-son data. At each iteration, a combination of the Pois-son observations with the denoised estimate from the pre-vious iteration is treated as scaled Poisson data and fil-tered through a VST scheme. Due to the slight mis-match between a true scaled Poisson distribution and thiscombination, a special exact unbiased inverse is designed.We present an implementation of this approach based onBM3D. With a computational cost only twice that of thenon-iterative scheme, the proposed algorithm provides sig-nificantly better quality, particularly at low SNR, outper-forming much costlier state-of-the-art alternatives.

Lucio AzzariDepartment of Signal ProcessingTampere University of [email protected]

Alessandro FoiDepartment of Signal ProcessingTampere University of Technology, [email protected]

MS74

Understanding Symmetric Smoothing FiltersThrough Expectation-Maximization

This talk addresses the question of why does a symmetricsmoothing filter yield better denoising performance than anon-symmetric smoothing filter. I will discuss our findingsthrough an expectation-maximization (EM) algorithm oflearning a model known as the product of Gaussians (PoG).I will also present an improved denoising algorithm basedon the new PoG model.

Stanley H. ChanElectrical and Computer EngineeringPurdue [email protected]

Todd Zickler, Yue LuHarvard SEAS

128 IS16 Abstracts


MS74

A Decomposition Framework for Image DenoisingAlgorithms

We present a novel framework for image denoising in whichthe components of a noisy image in a moving frame thatencodes its local geometry are denoised and then used togenerate a clean image. We show that the PSNR of thecomponents is higher than that of the image along imagecontours, providing justification for this framework. Ex-periments confirm the improvement when using this ap-proach in terms of both PSNR and SSIM.

Gabriela Ghimpet,eanuUniversitat Pompeu [email protected]

Thomas BatardDepartment of Information and CommunicationsTechnologiesUniversity Pompeu [email protected]


Stacey LevineDuquesne [email protected]

MS74

Turbo Denoising: Filter, Rinse, Recycle

We propose a new denoising algorithm for camera pipelinesand other photographic applications. We aim for a schemethat is (1) fast enough to be practical even for mobile de-vices, and (2) handles content dependent noise that is morerealistic for real camera captures. Our scheme consists ofa simple two-stage non-linear processing. We introduce anew form of boosting/blending which proves to be very ef-fective in restoring the details lost in the first denoisingstage. We also employ IIR filtering to significantly reducethe computation time. Further, we incorporate a novelnoise model to address for the content dependent noise.For realistic camera noise, our results are competitive withBM3D, but with nearly 400 times speedup.

Tak-Shing WongGoogle [email protected]


Hossein TalebiGoogleUniversity of California, Santa [email protected]

MS75

Selection Criterion for Source Encoding Weights in

Nonlinear Inverse Problems with Large Data

We introduce a method to systematically select amongrandom encoding weights, for inverse problem with mul-tiple right-hand sides, when these weights are sampledfrom the uniform spherical distribution. Drawing fromrecent developments in optimal experimental design forinfinite-dimensional Bayesian inverse problems, we intro-duce two Bayesian formulations of this weight selectionproblem. In addition, we rigorously formulate a bilevelHessian-constrained optimization problem for the compu-tation of weights that optimally verify our selection crite-rion.

Benjamin CrestelUniversity of Texas at AustinInstitute for Computational Engineering and [email protected]

Alen AlexanderianNC State [email protected]

Georg StadlerCourant Institute for Mathematical SciencesNew York [email protected]

Omar GhattasThe University of Texas at [email protected]

MS75

A Randomized Misfit Approach for Data Reduc-tion in Large-Scale Inverse Problems


Ellen LeUniversity of Texas at Austin - [email protected]

MS75

A Parametric Level Set Approach to the AirborneElectromagnetic Inverse Problem

We propose a method to invert time or frequency domainairborne electromagnetic data using a parametric level setapproach. This problem is computationally intensive dueto its expansive domain size and multitude of source loca-tions. Our approach reduces the parameter space by recov-ering best-fitting skewed Gaussian ellipsoids that representelectrical conductivity anomalies of interest. The packageis developed in Julia and can be combined with conven-tional voxel based inversions to resolve additional smoothbackground features.

Michael S. McMillanUniversity of British [email protected]

Eldad HaberDepartment of MathematicsThe University of British [email protected]

Christoph Schwarzbach, Douglas OldenburgUniversity of British [email protected], [email protected]

IS16 Abstracts 129

Eliot HolthamComputational Geosciences, [email protected]

MS75

Fast Algorithms for Hyperspectral Diffuse OpticalTomography with Many Measurements

Diffuse Optical Tomography is an imaging modality whichuses measurements obtained using near-infrared light toimage highly turbid media. The measurements can be usedto produce spatial maps of parameters of interest by solvingan ill-posed inverse problem. Solving the full nonlinearproblem is very computationally expensive particularly formeasurements at several wavelengths. The algorithms wepropose bring down the computational cost by 1-2 ordersof magnitude.


Misha E. KilmerMathematics DepartmentTufts [email protected]

Eric MillerTufts [email protected]

MS76

Bilevel Parameter Learning for Higher-Order TotalVariation Regularisation Models

We consider a bilevel optimisation approach for parame-ter learning in higher order TV image reconstruction mod-els. Differentiability properties of the solution operator areverified and an optimality system derived. Based on theadjoint information, a quasi-Newton algorithm is proposedfor the numerical solution of the problems. We proposea new cost functional, based on a Huber regularised TV-seminorm. Thanks to the bilevel optimisation framework,a detailed comparison between TGV2 and ICTV is pre-sented.




MS76

Learning Variational Models for Image Reconstruc-tion

Existing image reconstruction methods are based on sim-ple regularizers such as sparsity in the wavelet domain orTotal Variation (TV). However, these simple and hand-crafted regularizers make assumptions on the underlyingimage statistics. We propose to learn proper regularization

of variational models, i.e. a set of filters and correspondingpenalty functions, and focus on its application to MRI re-construction. Our approach overcomes several limitationsof existing reconstruction methods such as parameter se-lection problems.

Kerstin HammernikGraz University of TechnologyInstitut fur Maschinelles Sehen und [email protected]

Florian KnollNew York University School of [email protected]

Thomas PockInstitute for Computer Graphics and VisionGraz University of [email protected]

MS76

Should You Derive or Let the Data Drive? An Op-timization Framework for Model Mis-specificationCorrection

While “all models are wrong...”, it is often possible to de-duce a correction for a model, that offers improved predic-tive and / or prescriptive capabilities. In this talk we shallpresent a hybrid first-principles, data-driven optimizationframework for model mis-specification correction. The ap-proach balances between model fidelity, model complexity,and virtues associated with both the correction and thecorrected forms.

Lior HoreshMathematical Sciences & AnalyticsIBM [email protected]

Remi [email protected]

Haim AvronTel Aviv [email protected]

Karen E. WillcoxMassachusetts Institute of [email protected]

MS76

Computational Regularization in Learning and In-verse Problems

High dimensional estimation problems from random datarequire ever more efficient algorithms. A key observa-tion towards this goal is that the computations shouldbe taylored to the estimation accuracy allowed by thedata. Based on this intuition we investigate methods ex-ploiting the trade-offs between estimation and computa-tional requirements. In particular, we focus on random-ized/iterative regularization methods where regularizationis achieved by early stopping. Results in the context ma-chine learning and inverse problems are discussed.

Silvia VillaDIMA, University of Genova, Italy

130 IS16 Abstracts

[email protected]

Lorenzo RosascoInstituto Italiano di Technologia andMassachusetts Institute of [email protected]

MS77

Learning the Structural Organisation of NeuralCircuits from Neuroimaging Data

We will present a computational and statistical frameworkto learn the structural organisation of neural circuits frommultimodal neuroimaging data. The method estimatestypical configurations of neural circuits in the form of acollection of curve and surface meshes, which represent themain components of the brain architecture. The estima-tion of the typical variability of this configuration within agroup of subjects include variations in the shape/geometryof the individual components, as well as the relative posi-tion of the white matter fiber tracts with respect to the greymatter structures, thus capturing changes in the structuralconnectivity. We will show that these modes of variabilityallow a better prediction of the presence of neurodevelop-ment disorders, such as Gille de la Tourette syndrome, thanmore traditional morphometric studies.

Stanley DurrlemanINRIAICM Brain and Spine [email protected]

Pietro GoriINRIAICM - Brain and Spine [email protected]

MS77

Brain Microstructure Characterization UsingSparse Bayesian Inference and Multi-compartmentModels Estimation

First, we demonstrate how sparsity can be introduced intoa recent multi-resolution algorithm (RubiX) to estimatewhite matter fiber orientations from compressed (under-sampled) diffusion MRI (dMRI) data. A sparse Bayesianalgorithm combines data acquired at different spatial res-olutions via a dictionary representation and priors whichleverage the dependence between fiber orientations, andthe spatial redundancy in data representation. Second, weintroduce a data fitting procedure for biophysical modelswhich relate quantities such as axonal radius and densityto the dMRI data by predicting signal in the intra- andextra-axonal compartments. Using variable projection andstochastic global search algorithms, we present an efficientand robust method to estimate axonal radii and densitiesfrom non-invasive dMRI data.

Christophe LengletDepartment of Electrical and Computer EngineeringUniversity of [email protected]

MS77

Thinking Outside the Voxel: A Joint Spatial-Angular Basis for Sparse Hardi Reconstruction

Sparse HARDI representations are of growing interest to

reduce the large number of diffusion signal measurements.With few exceptions, sparsifying bases are considered forq-space with additional constraints of spatial regularity. Inthis work, we propose a single joint spatial-angular basisrepresentation to model an entire HARDI dataset with anincreased level of sparsity. With a globally compressed rep-resentation we can redefine HARDI processing, diffusionestimation, and feature extraction and reduce acquisitiontime.

Evan SchwabJohns Hopkins [email protected]

MS77

Compressed Sensing of Multi-shell HARDI in Six-dimensional (k,q) Space

Compressed Sensing (CS) has been widely successful in re-ducing the acquisition time for standard structural imagessuch as MR and CT images. However, CS has not enjoyedthe same level of success in making multi-shell high an-gular resolution diffusion imaging (MS-HARDI) clinicallyviable. In this work, we propose a novel CS method forfast acquisition of MS-HARDI and thus making it clini-cally viable. The method is based on applying CS to the6D (k,q) space and directly achieving sparse reconstructionof the ensemble average propagators, which are probabilitydensity functions that capture the entire local diffusionalinformation.

Baba C. VemuriDepartment of Computer & Information Science andEngineeringUniversity of [email protected]

MS78

Multidimensional Iterative Filtering Method forthe Decomposition of High-Dimensional Non-Stationary Signals

Iterative Filtering, which is an alternative technique to theEmpirical Mode Decomposition algorithm for the decom-position of non-stationary and non-linear signals,has beenproved recently to be convergent for any L2 signal. Inthis talk we introduce its extension to higher dimensions,called Multidimensional Iterative Filtering algorithm, andwe show the performance of this new technique when ap-plied to the decomposition of syntectic and real life 2Dsignals.

Antonio CiconeUniversita degli studi dell’[email protected]

Haomin ZhouGeorgia Institute of [email protected]

MS78

Fast Algorithms for Elastic-Wave-Mode Separationand Vector Decomposition

Modern algorithms for seismic data analysis require anability to find a sparse transform or dictionary for seismicdata representation. We describe two methods, a slopedecomposition based on nonstationary autoregression and

IS16 Abstracts 131

the nonstationary seislet transform. In combination, thesetools provide a particularly sparse representation for mul-tidimensional seismic data and find practical applicationsin denoising and data reconstruction problems.

Sergey Fomel, Yangkang ChenUniversity of Texas at [email protected], [email protected]

MS78

Seismic Imaging with Extrapolated Low Frequen-cies

The band-limited nature of seismic data has been prohibit-ing full waveform inversion from practical success. We pro-pose two methods to extrapolate low frequencies from theband-limited data. The phase-and-amplitude tracking ap-proach performs extrapolation as a data processing step.The extended demigration approach extrapolates the lowfrequency via forward and adjoint Born imaging. Bothmethods are based on the non-dispersive media assump-tion.

Yunyue LiMassachusetts Institute of [email protected]

MS78

When Harmonic Analysis Meets Medicine

We will discuss some recent developments of applied har-monic analysis and their application to medical problems;in particular, the anesthesia/sedation/sleep analysis basedon different physiological signals and images.

Chen-Yun Lin, Hau-Tieng WuUniversity of [email protected]), [email protected]

MS79

A Computationally Efficient Levenberg-MarquardtAlgorithm and Its Application to Inverse Modeling

Inverse modeling seeks transitivity field given measure-ments of hydraulic heads. However, practical prob-lems are often large scale, and conventional methodscan be computationally expensive. We have developeda new, computationally-efficient Levenberg-Marquardtmethod for solving large-scale problems. Our method isbased on a recycled-Krylov subspace technique. We applyour method to invert for a random transitivity field in par-allel and obtain a significant speedup. Therefore, our newinversion method is a powerful tool for large-scale applica-tions.

Youzuo LinLos Alamos National [email protected]

Dan O’Malley, Velimir V. VesselinovLos Alamos National [email protected], [email protected]

MS79

Choice of TV Regularization Parameter for Elec-trical Resistance Tomography

In subsurface Electrical Resistance Tomography an image

of electrical conductivity profiles is recovered from appar-ent resistivity measurements. L2 regularization smoothsconductivity estimates, so Total Variation is used to detectsharp boundaries. The artifacts produced by TV regular-ization are mitigated by focusing on regularization param-eter choices that result in identifying true anomalies. Themethods are tested on measurements at the Boise Hydro-geophysical Research site, a field laboratory where conduc-tivity regions are well understood.

Jodi MeadBoise State UniversityDepartment of [email protected]

Hank HetrickGeoscience DepartmentBoise State [email protected]

MS79

Hybrid and Iteratively Reweighted Regularizationfor Edge Enhancing Reconstructions

Tikhonov regularization for projected solutions is consid-ered as the initial step in edge enhancing regularizers, byiterative reweighting and Split Bregman (SB) techniques.Determination of the L2 regularization parameter is foundusing unbiased predictive risk estimation extended for theprojected problem. The initial projected solution is en-hanced by SB or TV Tikhonov iterations. The iterativeapproach stabilizes and it robust to the size of the pro-jected problem and the determination of the regularizationparameter. Examples for inverting geophysical data illus-trate the effectiveness of the approach for large scale data.

Rosemary A. RenautArizona State UniversitySchool of Mathematical and Statistical [email protected]

Saeed VatankhahUniversity of Tehran, [email protected]

MS79

Spatio-Spectral Background Estimation in RemoteSensing Imagery

We investigate several approaches for estimating thetarget-free background at a given pixel in a remotely sensedimage, based on both the local neighborhood around thatpixel and on the global context of the full image. Since weseek this background estimate at every pixel in the image,and since we do not want to include the potentially target-contaminated pixel in this estimate, the problem is a kindof hybrid between noise reduction and in-painting.

James TheilerSpace and Remote Sensing SciencesLos Alamos National [email protected]

Brendt WohlbergLos Alamos National Laboratory

132 IS16 Abstracts

[email protected]

MS80

Bilevel Optimization for a Generalized Total-Variation Model

Analytical and, in particular, practical aspects for a con-fidence based automated choice rule for the regulariza-tion weight in a generalization of the renowned total vari-ation regularization model in image restoration are dis-cussed. For an associated bilevel optimization problem,a projection-type algorithm is introduced and a report onthe qualitative behavior of the new model is given.

Michael HintermullerHumboldt-University of [email protected]

MS80

The Primal-Dual Hybrid Gradient Method forSemiconvex Splittings

In this work we analyze a recent reformulation of theprimal-dual hybrid gradient method which makes it ap-plicable to nonconvex regularizers. In particular, we in-vestigate variational problems for which the energy to beminimized can be written as G(u) + F (Ku), where G isconvex, F semiconvex and K a linear operator. We studythe method and prove convergence in the case where thenonconvexity of F is compensated by the strong convex-ity of the G. The convergence proof yields an interestingrequirement for the choice of algorithm parameters, whichwe show to not only be sufficient, but necessary. Addi-tionally, we show boundedness of the iterates under muchweaker conditions. Finally, we demonstrate effectivenessand convergence of the algorithm beyond the theoreticalguarantees in several numerical experiments.

Thomas MollenhoffTechnische Universitat [email protected]

Evgeny StrekalovskiyTechnical University of [email protected]



MS80

On the Global Minimizers of a Family of L0 Penal-ized Models

Log-likelihood data terms combined with L0 penalty arewidely used in imaging. A central question in optimizationis to know whether these problems admit global minimiz-ers. We will answer this question for a wide family of prob-lems. The answer is not always positive even though algo-rithms can give satisfying results. In those cases, a betteradapted (and better justified) formulation of the originalproblem might yield a consistent problem.

Mila Nikolova

Centre de Mathematiques et de Leurs Applications(CMLA)ENS de Cachan, CNRS, PRES [email protected]

MS80

Nonconvex ADMM: Its Convergence and Applica-tions

ADMM has been surprising us with a lot of success atsolving non-convex optimization problems in the litera-ture! They, but not limited to, the minimization of lq(0 < q < 1) quasinorm, Schatten-q quasinorm, SCAD,bi-linear, and bi-convex functions, as well as those subjectto orthogonality and sphere constraints. We provide in-sights toward when and how ADMM converges on convexand non-convex problems with multiple blocks. We showthat, roughly speaking, if the “last block” is smooth andits objective function “almost prox-regular” (by adding aquadratic function, the objective function becomes convexexcept for a small set) and if all the constraint coefficientmatrices stay in the span of the last one, then ADMMprovably converges. Note that all functions in the objec-tive can be nonconvex! Also note that the convergence ofADMM extending to multiple blocks is ensured under ourcondition. In spite of the counter example by Chen et al,ADMM can work well for three or more blocks. Throughexamples, we highlight that the ADMM can converge onproblems that ALM (the augmented Lagrangian method)diverges. We compare our work to other recent results ofnonconvex methods. Finally, we present applications ofnon-convex ADMM with provable convergence and goodperformance.

Yu WangXian Jiaotong [email protected]


Jinshan ZengJiangxi Normal [email protected]

MS81

Regularization of Linear Inverse Problems with To-tal Generalized Variation

Total generalized variation (TGV) regularization has foundmany successful applications in mathematical image pro-cessing, quite often in the context of linear inverse prob-lems such as, e.g., MRI reconstruction. We study essentialfunctional analytic properties of TGV and put its regu-larization performance for general linear inverse problemson a rigorous basis. In particular, we derive non-standardconvergence properties for vanishing noise level that resultfrom the cascadic multi parameter setting that is inherentto TGV.

Martin HollerUniversity of Graz

IS16 Abstracts 133

[email protected]

MS81

What Do Regularisers Do?

Which regulariser is the best? Is any of them any good? Dothey introduce artefacts? What other qualitative proper-ties do they have? Based on an analytical study of bileveloptimisation, in a recent work with J. C. De Los Reyesand C.-B. Schnlieb, we have derived natural conditions onthe data, showing regularisation to indeed improve images.I will discuss these results with a brief review on recentprogress in the analytical study of artefacts.


Carola-Bibiane SchonliebDepartment of Applied Mathematics and TheoreticalPhysics (DUniversity of [email protected]


MS81

Anisotropic Mumford-Shah Model for Detection ofThin Structures

This talk is devoted to the Mumford-Shah model for thesegmentation problem of thin structures, like tubes or thinplates in a 3-D image. A geometric interpretation of theparameters and necessary conditions will be given. If itcan not be satisfied, a different approach will be proposed.The main ingredient is the introduction of an anisotropicsetting. The analysis of this new model will be done, withgamma-convergence approximations and regularity resultsfor the minimizers.

David VicenteUniversity of [email protected]

MS81

Retinex by Higher Order TVL1 Decomposition

We propose a reflectance and illumination image decompo-sition model via high-order total variation and L1 decom-position. The proposed convex variational model can effec-tively decompose the gradient field of images into salientedges and relatively smoother illumination field throughthe first- and second-order total variation regularizations.Numerical experiments show the strength of the proposedmodel with applications to Retinex illusions, bias field re-moval, and color image correction.

Jingwei LiangEcole Nationale Superieure d’Ingenieurs de Caen, [email protected]

Xiaoqun ZhangShanghai Jiao Tong University

[email protected]

MS82

Passive Source Geolocation


Margaret CheneyColorado State [email protected]

MS82

Multiscale Approach to Synthetic Aperture Radar

We consider Synthetic Aperture Radar (SAR) image for-mation in the situation when the propagation medium iscomplex. We carry out a scaling analysis. We discuss howdifferent noise contribution and wave configuration param-eters affect resolution.

Knut SolnaUniversity of California at [email protected]

MS82

Synthetic Aperture Imaging of Direction and Fre-quency Dependent Reflectivities

We propose a synthetic aperture imaging methodology thataccounts for directional and frequency dependent reflectiv-ities. Our approach uses �1 minimization and is based ondata segmentation in array sub-apertures and frequencysub-bandwidths. We present an analysis of this approachand asses its performance in an X-band radar regime. Thisis joint work with Liliana Borcea, Miguel Moscoso andGeorge Papanicoloau.

Chrysoula TsogkaUniversity of Crete and [email protected]

MS82

Transionospheric Synthetic Aperture Imaging

Earth’s ionosphere may adversely affect the spaceborneSAR images, because the dispersion of radio waves causesdistortions of radar signals that cannot be automaticallyaccounted for by the matched filter. We propose to build aredundancy into the SAR dataset by probing the terrain,and hence the ionosphere, on two distinct carrier frequen-cies. It allows us to reconstruct the parameters of the iono-sphere needed for correcting the filter and improving thequality of the image.

Semyon V. TsynkovDepartment of MathematicsNorth Carolina State [email protected]

MS83

Harvesting Nature: from Computational Imagingto Optical Computing

We investigate how a simple experiment of imaging withcoherent light through a layer of multiply scattering ma-terial can be seen as an idealized physical implementation

134 IS16 Abstracts

of compressed sensing. In reverse, we show how this sys-tem can be used as a computing device that provides alarge number of random projections of incoming data -and demonstrate its effectiveness for classification tasks,e.g. physically approximating a given kernel.

Laurent DaudetParis Diderot [email protected]

MS83

Photon-Efficient Reflectivity and Depth Imagingunder Significant Ambient Light

LIDAR systems use single-photon detectors to enable long-range reflectivity and depth imaging. By exploiting a Pois-son observation model and the typical structure of naturalscenes, first-photon imaging demonstrates the possibilityof accurate LIDAR with only 1 detected photon per pixel,where half of the detections are due to (uninformative)ambient light. Here we present spatially adaptive noisecensoring to achieve similar performance when 90% of de-tections are due to ambient light, potentially further in-creasing range.

Vivek K. GoyalBoston [email protected]

MS83

Macroscopic Fourier Ptychography

Recent advances in ptychography have demonstrated thatone can image beyond the diffraction limit of the objec-tive lens in a microscope. We demonstrate a similar ap-proach to imaging beyond the diffraction limit at long-ranges. We show that an appropriate phase retrieval basedreconstruction algorithm can be used to effectively recoverthe lost high-resolution details from multiple low-resolutionacquired images. Our experimental results from our proof-of-concept systems show resolution gains of 4x- 7x for realscenes.

Oliver CossairtNorthwestern [email protected]

Jason R. HollowayRice UniversityDepartment of Electrical [email protected]


Manoj SharmaNorthwestern [email protected]

Salman AsifRice [email protected]

Nathan MatsudaNorthwestern [email protected]

Roarke HorstmeyerCalifornia Institute of [email protected]

MS83

Lensless Imaging



MS84

Challenges and Opportunities in Space SituationalAwareness (SSA): An Air Force Perspective

With a rapidly increasing population of objects in space,the traditional Space Situational Awareness (SSA) con-struct from the Cold War era will no longer suffice. Mod-ernizing the Air Force SSA to meet the challenges of todayand tomorrow requires new technologies, applications andoperating constructs as well as an expanded engagementwith nations active in the space domain.

Thomas CooleyAir Force Research [email protected]

MS84

High-resolution Speckle Imaging Through StrongAtmospheric Turbulence

We demonstrate that high-resolution imaging throughstrong atmospheric turbulence can be achieved by ac-quiring data with a system that captures short exposure(speckle) images using a range of aperture sizes and thenusing a bootstrap multi-frame blind deconvolution restora-tion process that starts with the smallest aperture data.Our results suggest a potential paradigm shift in how weimage through atmospheric turbulence. No longer shouldimage acquisition and post processing be treated as twoindependent processes: they should be considered as inti-mately related.

Stuart JefferiesInstitute for AstronomyUniversity of [email protected]

Douglas HopeU.S. Air Force [email protected]

Michael HartUniversity of [email protected]


MS84

Image Reconstruction using Sparse Aperture Tech-

IS16 Abstracts 135

niques for SSA

We will discuss the use of long-baseline optical interfer-ometry for ground-based imaging of geosynchronous satel-lites. Aperture fill is achieved by collecting data with dif-ferent telescope-baseline configurations. Sparse samplingtechniques can be used to create images from fewer ob-servations and reduce the length of an imaging campaign.Simulation results from various reconstruction algorithmsare compared.

Robert ShivitzLockheed Martin Space Systems [email protected]

James Mason, Greg Feller, Sam ThurmanLockheed Martin Space Systems [email protected], [email protected],[email protected]

MS84

High Resolution Imaging of Geosats at Lowell Ob-servatory


Gerard von BelleLowell [email protected]

MS85

Tone Mapping and Gamut Mapping for Cinema

In this talk I will present recently proposed image process-ing techniques based on vision science that address two im-portant problems in the motion picture and TV industries:tone mapping (making high dynamic range images suitablefor standard dynamic range displays) and gamut mapping(modifying the color gamut of images so that they prop-erly fit the color capabilities of a given display). Website:http://ip4ec.upf.edu/


MS85

Texture Synthesis and Transfer Using Convolu-tional Neural Networks

We introduce a new model of natural textures based on thefeature spaces of convolutional neural networks optimisedfor object recognition. Extending this framework to tex-ture transfer, we introduce A Neural Algorithm of ArtisticStyle, which can separate and recombine the image con-tent and style of natural images. Finally, we demonstratehow this allows us to produce new images of high per-ceptual quality that combine the content of an arbitraryphotograph with the appearance of numerous well-knownartworks.

Leon A. GatysUniversitat TubingenCenter for Integrative Neuroscience - Betghelab [email protected]

Alexander S. Ecker, Matthias BethgeUniversitat TubingenCenter for Integrative Neuroscience - Bethgelab

[email protected],[email protected]

MS85

Video Temporal Consistency

In this talk, I will present my work on temporal consistencyin videos. I will first briefly review my past work on thistopic that sought to extend the notion of Gaussian filteringto the temporal domain and later formulated a curvatureflow filter in the space of functions. Then, I will presentin more details my most recent project that processes theimage gradients. This technique is simple, applicable toa wide range of effects, and has the advantage of beingamenable to a formal analysis in the Fourier domain. web-site: http://liris.cnrs.fr/ nbonneel/consistency/

Sylvain ParisAdobe Systems Inc.Cambridge Innovation [email protected]

Nicolas BoneelCNRS [email protected]

MS85

Nonlocal Image Editing

We introduce a new image filtering tool, based on the spec-trum of global image affinities. The global filter derivedfrom a fully connected graph representing the image, can beapproximated by its leading eigenvectors. These orthonor-mal eigenfunctions are highly expressive of the coarse andfine details in the underlying image, thus endowing the fil-ter with a number of important capabilities, such as sharp-ening, smoothing and tone manipulation.

Hossein TalebiGoogleUniversity of California, Santa [email protected]


MS86

Image Restoration with Shannon Total Variation

Usual discretizations by means of finite differences for to-tal variation (TV) based energy minimization models gen-erally lead to images difficult to interpolate at sub-pixelscales. We propose a new Fourier-based estimate (calledShannon total variation), which behaves much better interms of isotropy, artifact removal, and sub-pixel accuracy.This variant can be used with dual algorithms, and de-livers images that can be easily interpolated without arti-facts. Illustrations are provided for several classical TV-based restoration models.

Remy AbergelUniversite Paris [email protected]

Lionel MoisanParis 5

136 IS16 Abstracts

[email protected]

MS86

A Variational Approach for Color Image Enhance-ment

In this work, a novel approach for color image contrast en-hancement is proposed. It is based on a variational frame-work increasing the global contrast. In the literature, themethods may over-contrast the results, and/or produceHue distortions. The proposed approach makes the userable to control the contrast level intuitively, as for instancethe scale of the enhanced details. Moreover, it avoids largemodifications of the image histograms and thereby pre-serves the global illumination of the scenes. This techniqueis extended to color images into a variational frameworkthat preserves the Hue. The color model is solved witha hybrid primal-dual algorithm which requires no post- orpre-processing. This is a joint work with Fabien Pierre,Aurelie Bugeau, Gabriele Steidl, and Vinh-Thong Ta.

Jean-Francois AujolIMB, CNRS, Universite Bordeaux [email protected]

MS86

Semi-Inner-Products for Convex Functionals andTheir Use in Image Decomposition

Semi-inner-products in the sense of Lumer are extendedto convex functionals. A general expression for the one-homogeneous case is given. This facilitates the analysisof total variation and higher order functionals like total-generalized-variation (TGV). An angle between functionscan be defined, where relations of the angle to the Breg-man distance are shown. This construction is used to statea sufficient condition for a perfect decomposition of twosignals using the spectral one-homogeneous framework.


MS86

Image Deblurring Via Total Variation Based Struc-tured Sparse Model Selection

In this talk, we study the image deblurring problem basedon sparse representation over learned dictionary whichleads to promising performance in image restoration inrecent years. However, the commonly used overcompletedictionary is not well structured. This shortcoming makesthe approximation be unstable and demand much com-putational time. To overcome this, the structured sparsemodel selection (SSMS) over a family of learned orthogo-nal bases was proposed recently. In this paper, We furtheranalyze the properties of SSMS and propose a model fordeblurring under Gaussian noise. Numerical experimentalresults show that the proposed algorithm achieves compet-itive performance. As a generalization, we give a modifiedmodel for deblurring under salt-and-pepper noise. The re-sulting algorithm also has a good performance.

Tieyong ZengDepartment of MathematicsHong Kong Baptist University

[email protected]

MS87

Analytic Approaches to Study the Chronnectome(time-Varying Brain Connectivity)

Recent years have witnessed a rapid growth in moving func-tional magnetic resonance imaging (fMRI) connectivity be-yond simple scan-length averages into approaches that cap-ture time-varying properties of connectivity. In this per-spective we use the term chronnectome to describe suchmetrics that allow a dynamic view of coupling. We dis-cuss the potential of these to improve characterization andunderstanding of brain function, which is inherently dy-namic, not-well understood, and thus poorly suited to con-ventional scan-averaged connectivity measurements.

Vince CalhounElectrical and Computer EngineeringUniversity of New [email protected]

MS87

Using Complementary Assessments of Structuraland Functional Brain Connectivity to Gain Insightsinto Neurodevelopment

Neuroimaging technologies provide complementary mea-sures that need to be considered in concert to gain a fullunderstanding of the elements that influence the emergenceof brain function. I will describe the strengths and weak-nesses of these complementary approaches that guide thedevelopment of model systems when assessing brain func-tion at the macroscopic scale. We will describe how cap-turing development across different temporal and spatialscales will inform our knowledge of emerging functionalbrain dynamics.

Julia StephenThe Mind Research [email protected]

MS87

Modeling and Integration of Imaging and Ge-nomics Data

I will present computational approaches on the integrationof multi-scale genomic and imaging data. First, I will showhow to correlate genomic and image data with sparse CCAfor biomarker detection. Second, I will discuss how to in-tegrate genomic, imaging and protein-protein interactionnetworks using a collaborative low rank regression model.Finally, I will present examples on improved diagnosis ofschizophrenia with these integrative models.

Yu-Ping WangTulane [email protected]

MS87

Neural Oscillations and Dynamic Functional Con-nectivity Analysis with MEG

Large populations of cortical neurons often exhibit coordi-nated electrical fluctuations, and these so-called neuronaloscillations are known to be critical for cognitive process-ing and neural computation. This presentation will de-scribe the latest in oscillatory analysis methods, especially

IS16 Abstracts 137

as applied to magnetoencephalography (MEG) data. Re-cent findings in the context of human motor control, work-ing memory, attention, and neurological disease will be dis-cussed, as will the directed dynamic functional connectivityanalyses that oscillatory analysis methods often enable.

Tony W. WilsonUniversity of Nebraska Medical [email protected]

MS88

On the Analysis of Multicomponent Images

The concept of multicomponent signals, defined as super-positions of AM/FM waves, plays a key role in the analysisof non-stationary signals in one dimension. Recent meth-ods have been developed for analyzing and decomposingthose signals, such as the empirical mode decompositionor the synchrosqueezed wavelet transform. I will presentin this talk several extensions of these techniques in dimen-sion 2, trying to underline their potential interest for theadaptive analysis of images.

Thomas OberlinUniversity of [email protected]

MS88

Conceft: Concentration of Frequency and Time Viaa Multitapered Synchrosqueezed Transform

A new method is proposed to determine the time-frequencycontent of time-dependent signals consisting of multiple os-cillatory components, with time-varying amplitudes andinstantaneous frequencies. Numerical experiments as wellas a theoretical analysis are presented to assess its effec-tiveness.

Ingrid DaubechiesDukeDepartment of [email protected]

Yi WangSyracuse [email protected]

Hau-Tieng WuUniversity of [email protected]

MS88

Canvas Texture Analysis for Art Investigation

This talk introduces new techniques for the study of arthistory and art conservation. The first part introducesa new technique for separating canvas from digital pho-tographs and X-ray images of paintings on canvas. It com-bines the cartoon-texture decomposition and an adaptivethresholding to isolate canvas. The second part will in-troduce a new canvas thread counting method based on2D synchrosqueezed transforms that offers fine scale weavedensity and thread angle information for the canvas.

Haizhao YangDuke UniversityMath Dept, Duke [email protected]

Bruno CornelisDuke [email protected]

Jianfeng LuMathematics DepartmentDuke [email protected]

Lexing YingStanford [email protected]


MS88

Source Separation in Art Analysis: Digital CradleRemoval in X-Ray Images of Art Paintings

We propose a source separation algorithm for cradling ar-tifacts removal in X-ray images of panel paintings, signif-icantly improving X-ray image readability for art experts.The algorithm consists of grayscale inconsistency correc-tion, based on physical properties of X-ray imaging, andcradling wood grain extraction, where a sparse Bayesianfactor model is trained for blind separation of cradling andpainting panel wood grain mixture, which is obtained asthe texture of X-ray images from Morphological Compo-nent Analysis.

Rujie Yin, Bruno CornelisDuke [email protected], [email protected]

Gabor FodorVrije Universiteit, [email protected]


David DunsonDuke [email protected]

MS89

On the Well-Posedness of Non-Convex Total Vari-ation

Total variation models based on non-convex energies havebeen introduced to provide better match for observed gra-dient statistics in real-life images. In the functional ana-lytical settings, these models are however highly ill-posed.For restoring well-posedness, I will discuss ideas based onmulti-scale analysis.


MS89

Bilevel Optimization of Nonconvex �q-Models in

138 IS16 Abstracts

Image Processing

This work concerns bilevel optimization of nonconvex �q-models. Based on the analysis of local minimizers of thenonconvex �q-model (as the lower-level problem), we im-pose qualification conditions for replacing the lower-levelproblem by its first-order optimality condition. A smooth-ing homotopy approach is proposed for the numerical solu-tion of the bilevel problem, where each smoothed reducedsubproblem is handled by a projected BFGS method. Nu-merical results on selected imaging applications are pre-sented to support our theoretical findings.

Tao WuHumboldt-University of [email protected]

Michael HintermullerDepartment of Mathematics, Humboldt-University [email protected]

MS89

Proximal Iterative Hard Thresholding Methods forWavelet Frame Based Image Restoration

The iterative thresholding algorithms were primarily pro-posed in the literature for solving wavelet based linear in-verse problems, including image restoration problems withsparsity constraint. The analysis of iterative soft thresh-olding algorithms has been well studied and inspired muchof the work for divers applications and related minimiza-tion problems. However, iterative hard thresholding meth-ods are less understood due to its non-convexity and non-smoothness except some studies related to sparse signalrecovery and image restoration. In this work, we pro-pose two algorithms, namely extrapolated proximal itera-tive hard thresholding (EPIHT) algorithm and EPIHT al-gorithm with line-search (EPIHT-LS), for solving l0 normregularized wavelet frame balanced approach for imagerestoration. Under the Kurdyka- Lojasiewicz property the-oretical framework, we show that the sequences generatedby the two algorithms converge to a local minimizer withlinear convergence rate. Moreover, extensive numericalexperiments on sparse signal reconstruction and waveletframe based image restoration problems including CT re-construction, image deblur, demonstrate the improvementof l0-norm based regularization models over some prevail-ing models, as well as the computational efficiency of theproposed algorithms.

Chenglong BaoNational University of [email protected]


Zuowei ShenUniversity of WisconsinComputer Science [email protected]

Xiaoqun Zhang, Xue ZhangShanghai Jiao Tong University


MS90

Second-Order Edge-Penalization in the Ambrosio-Tortorelli Functional

In this talk we discuss a variant of the Ambrosio-Tortorellifunctional where the first-order penalization of the edgevariable v is replaced by a second-order term depending onthe Laplacian of v. This new energy provides an elliptic ap-proximation of the Mumford-Shah functional in the senseof Gamma- convergence and presents many advantages incomputational experiments, as we will show with severalexamples.

Teresa EspositoUniversity of [email protected]


Caterina Ida ZeppieriUniversity of [email protected]

MS90

Optimal Selection of the Regularisation Functionin a Localised TV-Model

A bilevel optimization approach for the automated selec-tion of a distributed regularization parameter in a totalvariation regularization based image restoration model isconsidered. While the lower level problem amounts to solv-ing a variant of the renowned Rudin-Osher-Fatemi model,but with local regularization effects, the upper level objec-tive is related to a statistics based variance corridor aroundthe ideal reconstruction. Besides the model and its math-ematical analysis, a numerical solution scheme is proposedand test results for image restoration including Fourier andwavelet transformations are reported on.

Michael HintermullerHumboldt-University of [email protected]

MS90

Analytical Aspects of Spatially Adapted TotalVariation Type Regularisation

Spatially adapted regularisation in image reconstructionhas been used in order to preserve details like texture andother highly oscillating features that are naturally presentin the image. The idea is to apply regularisation of differentstrength in different parts of the image by spatially varyingthe regularisation parameters. In this talk, we will studyanalytically the effect of the spatially varying parametersto the structure of solutions of total variation type regu-larisation.

Kostas PapafitsorosHumboldt University of [email protected]

Michael Hintermuller, Carlos RautenbergHumboldt-University of Berlin

IS16 Abstracts 139


MS90

Cosparse Image Recovery from Few TomographicProjections

We investigate the reconstruction problem of discrete to-mography and present a relation between image cosparsityand sufficient number of tomographic measurements for ex-act recovery similar to the settings in Compressed Sensing.Further, known quantisation levels are used as prior knowl-edge to improve recovery using techniques from the field ofdiscrete graphical models. Finally, regarding recovery al-gorithms, we focus on decomposition schemes that exploitthe problem structure and scale up to large problem sizes.

Stefania PetraUniversity of Heidelberg, [email protected]

MS91

Imaging with Intensity Cross Correlations and Ap-plication to Ghost Imaging

We analyze an imaging method called ghost imaging thatcan produce an image of an object by correlating the inten-sities measured by a high-resolution (multi-pixel) detectorthat does not view the object and a low-resolution (single-pixel) detector that does view the object. We clarify theroles of the partial coherence of the source that illuminatesthe object and of the scattering properties of the mediumthrough which the waves propagate.

Josselin GarnierUniversity Paris DiderotLaboratoire de Probabilites et Modeles [email protected]

MS91

Crack Detection in Thin Plates


Laure GiovangigliUniversity of California at [email protected]

MS91

Fluorescence Optical Tomography with Poissonnoise

We consider the fluorescence optical tomography problemin which one excites fluorophores distributed in a mulitplescattering medium with a boundary source at the excita-tion wavelength, and then measures the light emitted bythose excited fluorophores at the boundary. The objectiveis to reconstruct the distribution of fluorophores from thoseboundary measurements of the emitted light. In particu-lar, we investigate explicitly modeling Poisson noise in themeasurements. For that case, we develop a reconstructionmethod for a sparse distribution of fluorophores using theSparse Poisson Intensity Reconstruction ALgorithm (SPI-RAL). Through numerical experiments, we show highlyaccurate reconstructions using this method along with anonconvex �p (p < 1) penalty term even with nontrivial

amounts of measurement noise.

Lasith AdhikariApplied Mathematics UnitUniversity of California, [email protected]

Arnold D. KimDepartment of MathematicsStanford [email protected]

Roummel F. MarciaUniversity of California, [email protected]

MS91

Imaging Point Sources in Unknown Environments

Reconstructing point sources from boundary or far-fieldmeasurements has many practical applications. There havebeen extensive studies on the reconstruction problem in ho-mogeneous media and known inhomogeneous media. Westudy here two point source identification problems in anunknown smooth inhomogeneous medium. The first one isbased on the Helmholtz equation while the second one isbased on the transport equation (and its diffusion approx-imation). We present some stability results for the recon-struction, for instance, the stability of the reconstructedquantities with respect to changes of the medium, as wellas some numerical simulations with synthetic data. This isa joint work with Yimin Zhong of UT Austin.

Kui Ren, Yimin ZhongUniversity of Texas at [email protected], [email protected]

MS92

Accelerated Douglas-Rachford Methods forConvex-Concave Saddle-Points Problems andApplications in Imaging

We discuss basic and accelerated versions of the Douglas-Rachford (DR) splitting method for the solution of convex-concave saddle-point problems that arise in variationalimaging. While the basic DR iteration admits weak andergodic convergence with rate O(1/k) for restricted primal-dual gaps, acceleration enables, under appropriate strongconvexity assumptions, to obtain convergence rates ofO(1/k2) and O(qk) for 0 < q < 1. The methods are ap-plied, numerically, to non-smooth and convex variationalimaging problems, such as total-variation denoising.


Hongpeng SunRenmin University of ChinaInstitute for Mathematical [email protected]

MS92

A Three-Operator Splitting Scheme and its Opti-mization Applications

In this talk, we introduce a new splitting scheme that ex-

140 IS16 Abstracts

tends the Douglas-Rachford and forward-backward split-ting schemes to monotone inclusions with three operators,one of which is cocoercive. We discuss why this algo-rithm works, derive several special cases, including a sim-ple three-block ADMM algorithm, and introduce an accel-eration that achieves the optimal rate of convergence forstrongly monotone inclusions. Finally, we discuss severalapplications and future research directions.

Damek DavisUniversity of California, Los [email protected]


MS92

Gradient Sliding for Saddle Point Problems

We consider a class of nonsmooth optimization problemwith saddle point structure. In order to compute an ap-proximate solution to the saddle point problem, we proposetwo novel first-order methods, namely the mirror-prox slid-ing algorithm and the accelerated gradient sliding methodwith smoothing. Both propose methods could skip thecomputation of the gradient of the smooth component fromtime to time, so that the number of gradient evaluations isbounded by O(

√1/ε), while achieving a O(1/ε) complex-

ity bound for solving SPP. As a byproduct, the proposedAGS algorithm can solve a class of smooth composite op-timization problem, and skipping the gradient evaluationof one of the smooth component regularly, while achievinga O(

√1/ε) complexity.

Guanghui LanDepartment of Industrial and SystemsUniversity of [email protected]

Yuyuan OuyangDepartment of Mathematical SciencesClemson [email protected]

MS92

Convergence Analysis for a Randomized Multi-block ADMM and Its Applications

Global convergence and the rate of convergence for twoblock ADMM has been well established. However, a directextension to more than two blocks may fail to converge.This talk will present a randomized version of the ADMMfor handling general multiblock problem with general lin-ear constraints. We will establish a sublinear convergenceresult for the general convex case and a linear convergenceresult for the strongly convex case (without smoothnessrequirement). The algorithm and its convergence resultsare further generalized to a problem setting where the ob-jective involves stochastic multiblock functions. Numericalexperiments will be shown on large-scale quadratic pro-grams and also problems from machine learning and imageprocessing.


Xiang GaoISyE, University of [email protected]

Shuzhong ZhangDepartment of Industrial & Systems EngineeringUniversity of [email protected]

MS93

Multiframe Blind Deconvolution for ImagingThrough Strong Atmospheric Turbulence


Brandoch CalefBoeing [email protected]

MS93

High-Resolution Imaging of Satellites with andWithout Adaptive Optics

Attainment of diffraction-limited resolution and highsignal-to-noise ratio in images of space-based objects evenwhen observed with adaptive optics (AO) is only possiblein conjunction with subsequent deconvolution. Our aim isto develop deconvolution strategy which is reference-less,i.e., no calibration PSF is required, free of hyperparam-eters, extendable to longer exposures, and applicable toimaging with adaptive optics. The theory and resultingdeconvolution framework were validated using simulationsand real data from the 3.5m telescope at Starfire OpticalRange.

Szymon GladyszFraunhofer Institute of [email protected]

MS93

Reconstruction and Enhancement of Astronomicaland Satellite Images Obtained Using Adaptive Op-tics

The Starfire Optical Range (SOR) has been collectingsatellite images for several years using adaptive optics tocorrect for atmospheric distortions in real time. In thispresentation, we will briefly review different techniques foratmospheric compensation of satellite imagery, includingtilt and higher order correction. We will also discuss dif-ferent techniques for sharpening images and for enhancingthe presentation of the imagery to the user. These applica-tions are used both for real-time image correction as wellas post-capture image correction.

Robert Johnson, Lee KannAir Force Research [email protected], [email protected]

MS93

3D Snapshot Imaging Via Rotating Psf for SpaceSurveillance

By placing a carefully designed spiral phase mask in theaperture of an imager, we may exploit the angular mo-mentum of light to encode the axial distance of a pointsource in the rotation of the point spread function (PSF).Such rotating-PSF-based imagers can acquire unresolved

IS16 Abstracts 141

sources in a large imaging volume in a single snapshot withhigh 3D localization accuracy, which can be employed forthe monitoring of the debris field near space assets.

Sudhakar PrasadUniversity of New [email protected]

MS94

Removing Camera Shake Via Fourier Burst Accu-mulation

Camera shake deblurring is typically addressed by solvingan inherently ill-posed deconvolution problem. If the pho-tographer takes a multi-image burst, we show that it is pos-sible to combine them to get a clean sharp version. The al-gorithm is strikingly simple: it performs a Fourier weightedaverage, with weights depending on the Fourier spectrummagnitude. The rationale is that camera shake has a ran-dom nature and thus frames are differently blurred.

Mauricio DelbracioDuke UniversityElectrical & Computer [email protected]

Guillermo SapiroDuke [email protected]

MS94

Revisiting Total Variation Blind Deconvolution

We will revisit progress on blind deconvolution in the pastfew decades. We will highlight what we have learned aboutthe problem formulation and, in particular, the choice ofregularization prior. The presentation will focus more onrecent progress with Variational Bayesian and Maximum aPosteriori methods. We will compare different approachesand illustrate what differences have a measurable effect onthe image deblurring performance.

Paolo FavaroUniversitat BernComputer Vision [email protected]

Daniele PerroneUniversitat [email protected]

MS94

Energy-Optimized Imaging

Programmable coding of light between an active sourceand a sensor has enjoyed broad use in 3D sensing andcomputational imaging applications. Little is known, how-ever, about how to utilize the source’s energy most ef-fectively. In this talk, we discuss a novel framework tomaximize energy efficiency by “homogeneous matrix fac-torization.” Our framework yields energy-optimized codesthat respect the physical constraints of modern projec-tors and has led to an extremely efficient depth camera—able to operate robustly even in direct sunlight with verylow power. Website: http://www.dgp.toronto.edu/ mo-toole/energyefficientimaging.html

Kiriakos Kutulakos

University of TorontoComputer [email protected]

Matthew O’TooleDepartment of Computer ScienceUniversity of [email protected]

Supreeth Achar, Srinivasa NarasimhanThe Robotics InstituteCarnegie Mellon [email protected], [email protected]

MS94

Single Shot HDR Imaging Using A HyperpriorBayesian Approach

Patch models with a Bayesian approach such as PLEachieve state-of-the-art results in several image restorationproblems. Local patch models such as NLBayes yield state-of-the-art results for denoising, but become ill-posed forzooming, inpainting, debluring. We present a new frame-work that enables to use local priors for more general in-verse problems by including a hyperprior on the model pa-rameters. We apply this new framework to HDR imag-ing from a single snapshot with spatially varying exposure.website http://perso.enst.fr/∼gousseau/single shot hdr/

Cecilia AguerrebereDuke [email protected]

Andres AlmansaTelecom [email protected]

Julie DelonLTCI - Telecom ParisTech - [email protected]

Yann GousseauTelecom [email protected]

Pablo MuseFacultad de Ingeniera - Universidad de la [email protected]

MS95

Edge preserving image reconstruction for 3D mag-netic particle imaging

Magnetic Particle Imaging [B. Gleich, J. Weizenecker, To-mographic imaging using the nonlinear response of mag-netic particles, Nature, 2005] is an imaging modality wherethe concentration of magnetic nanoparticles is determinedby measuring their non-linear magnetization response to anapplied magnetic field. We propose fused lasso regulariza-tion for the image reconstruction as well as a near-isotropicdiscretization and derive a new minimization method basedon the generalized forward-backward splitting [H. Raguet,J. Fadili, and G. Peyre, A generalized forward-backwardsplitting, SIAM Journal on Imaging Sciences, 2013] andthe taut string algorithm [P. Davies and A. Kovac, Lo-cal extremes, runs, strings and multiresolution, Annals ofStatistics, 2001]. We will illustrate our approach with sev-

142 IS16 Abstracts

eral numerical examples as well as real experimental data.

Christina BrandtUniversity of Eastern [email protected]

Martin StorathEcole Polytechnique Federale de [email protected]

Martin Hofmann, Tobias KnoppUniversity Medical Center [email protected], [email protected]

Andreas WeinmannHelmholtzZentrum [email protected]

MS95

An Affine Invariant Similarity Measure for Non-Local Image Restoration

Many state-of-the-art methods employ a patch-based ap-proach for image restoration and inpainting. Such methodsare based on the phenomenon of self-similarity, usual inthe natural images, and a patch comparison measure thatexploits it. In this talk we will give an overview of a re-cently proposed affine invariant comparison measure whichautomatically transforms patches to compare them in anappropriate manner. We will illustrate the power of thistechnique on the image denoising problem.

Vadim Fedorov, Coloma BallesterUniversitat Pompeu [email protected], [email protected]

MS95

Path Optimization with limited sensing ability



Seong Jun KimGeorgia Institute of [email protected]

Haomin ZhouGeorgia Institute of TechnologySchool of [email protected]

MS95

Inverse Problems with TV-ICE regularization

We propose a new variant of the celebrated Total Variationimage denoising model, that provides results very similarto the Bayesian posterior mean denoising (TV-LSE) whileshowing a much better computational efficiency. This vari-ant is based on an iterative procedure which is proved tolinearly converge to a fixed point satisfying a marginal con-ditional mean property. We explore a generalization toimage restoration and propose several converging schemes.

The implementation is simple, provided numerical preci-sion issues are correctly handled. Our experiments are veryclose to those obtained with TV-LSE and avoids as well theso-called staircasing artifact observed with classical TotalVariation denoising.

Cecile LouchetMathematics DepartmentUniversity of Orleans, [email protected]

Lionel MoisanParis [email protected]

MS96

A hierarchical KrylovBayes iterative inverse solverfor MEG with physiological preconditioning

The inverse problem of MEG is formulated in Bayesianframework and a hierarchical conditionally Gaussian priormodel is introduced,including a physiologically inspiredprior model accounting for the preferred directions ofthe source currents. The hyperparameter vector con-sists of prior variances of dipole moments,following a non-conjugate gamma distribution with variable scaling andshape parameters. A point estimate of dipole momentsand their variances is computed using an iterative alter-nating sequential updating algorithm, shown to be glob-ally convergent. The solution is an approximation of thedipole moments using a Krylov subspace iterative linearsolver equipped with statistically inspired preconditioningand suitable termination rule. The shape parameters ofthe model are shown to control focality, and the scalingparameters can be adjusted to provide a statistically welljustified depth sensitivity scaling. Computed examples arepresented.

Daniela CalvettiCase Western Reserve UnivDepartment of Mathematics, Applied Mathematics [email protected]

Annalisa PascarellaIstituto per le Applicazioni del [email protected]

Francesca PitolliUniversity of Roma La [email protected]

Erkki SomersaloCase Western Reserve [email protected]

Barbara VantaggiUniversity of Roma La [email protected]

MS96

On Preconditioning Newton Method For PDEConstrained Optimization Problems

Solving an inverse problem with second order methods isoften prohibitive due to the computational overhead ofsolving the Hessian equation. Even though using Newton

IS16 Abstracts 143

methods provide better convergence rates, but this hiddencost usually outweighs the benefits. We will present novelmethods for preconditioning the Hessian equation for prob-lems with a variety of (nonlinear) parabolic constraints. Inparticular, we present results for a tumor growth problem,and show that significant speedups can be gained.

Amir GholaminejadPhD Student, Institute for Computational Engineeringand Sciences, University of Texas at [email protected]


MS96

Nonlinear Quantitative Photoacoustic Tomographywith Two-photon Absorption

Two-photon photoacoustic tomography (TP-PAT) is anon-invasive optical molecular imaging modality that aimsat inferring two-photon absorption property of heteroge-neous media from photoacoustic measurements. In thiswork, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients ina semilinear elliptic PDE, the mathematical model for thepropagation of near infra-red photons in tissue-like opticalmedia, from the internal absorbed energy data. We de-rive uniqueness and stability results on the reconstructionsof single and multiple coefficients, and perform numericalsimulations based on synthetic data to validate the theo-retical analysis.

Kui Ren, Rongting ZhangUniversity of Texas at [email protected], [email protected]

MS96

Reduced Order Modeling in Photoacoustic Tomog-raphy

Photoacoustic tomography combines a rich optical contrastwith the high resolution of ultrasound tomography. Math-ematically it is an ill-posed inverse coefficient problem for acoupled wave equation and diffusion equation pair. Sincethe wave speed is assumed to be constant, to acceleratethe inversion, we use a Hessian-based reduced order modelfor the wave equation. We demonstrate the computationalgains on a synthetic problem motivated from neuroscience.

Sarah VallelianStatistical and Applied Mathematical Sciences InstituteNorth Carolina State [email protected]


MS97

Joint Denoising and Distortion Correction of Scan-ning Transmission Electron Microscopy Images ofCrystalline Structures

Given a series of scanning transmission electron microscopy(STEM) images at atomic scale, we propose a novel method

that jointly estimates the direction dependent STEM dis-tortions in each image and reconstructs the underlyingatomic grid of the material by fitting the atoms with bumpfunctions. The resulting minimization problems are solvednumerically using Trust Region. The method’s perfor-mance is evaluated on both synthetic and real data andcompared to an established non-rigid registration basedmethod.

Benjamin BerkelsRWTH Aachen [email protected]

Benedikt WirthUniversitat [email protected]

MS97

2D Empirical Wavelets

Empirical wavelets were proposed recently as an alterna-tive of the Empirical Mode Decomposition (EMD). Wewill present 2D empirical wavelets for image processingapplications. We integrate the empirical philosophy intostandard 2D wavelet like transforms (2D tensor wavelets,Littlewood-Paley wavelets, Ridgelets and Curvelets) andshow that each case correspond different type of Fourierdomain partitionings.

Jerome GillesDepartment of Mathematics and StatisticsSan Diego State [email protected]

Giang TranThe University of Texas at [email protected]


MS97

Sparse Time-Frequency Decomposition for Signalswith Multiple Measurements

In this talk, we consider multiple signals sharing same in-stantaneous frequencies. This kind of data is very commonin scientific and engineering problems. To take advantageof this special structure, Based on the simultaneously spar-sity approximation and fast Fourier transform, we developan efficient algorithm. This method is very robust to theperturbation of noise. And it is applicable to the generalnonperiodic signals even with missing samples or outliers.In the tests include synthetic and real signals, the perfor-mances of this method are very promising.

Zuoqiang ShiTsinghua [email protected]

Thomas HouCalifornia Institute of [email protected]

MS97

2D-TV-VMD: Two-Dimensional Compact Varia-

144 IS16 Abstracts

tional Mode Decomposition

Decomposing images into spatially compact modes of wave-like nature makes components accessible e.g., for space-frequency analysis, demodulation, texture analysis, denois-ing, or inpainting. 2D-TV-VMD decomposes an image intomodes with narrow Fourier bandwidth; to cope with sharpboundaries we introduce binary support functions, maskingthe narrow-band modes for image re-composition. L1/TV-terms promote sparsity and spatial compactness. Restrict-ing to partitions, we perform image segmentation based onspectral homogeneity.

Dominique Zosso, Konstantin DragomiretskiyUniversity of California, Los AngelesDepartment of [email protected], [email protected]


Paul S. WeissUniversity of California, Los AngelesCalifornia NanoSystems [email protected]

PP1

A Hybrid Spatio-Frequency Approach for Delineat-ing Subsurface Structures in Seismic Volumes

Frequency-based edge detection methods such as phasecongruency are generally fast and accurate but are sensitiveto noise, and cannot capture subtle edges that are markedby a change in texture rather than a change in amplitude.On the other hand, spatial edge detection methods of tex-tured data such as the Gradient of Texture (GoT), that weproposed in 2014, are more robust to noise, but are lesslocalized in space, and are more computationally expen-sive. In this paper, we share a new hybrid spatio-frequencyedge detection method, and show its effectiveness in saltdome delineation on 3D seismic data from the North SeaF3 Block.

Yazeed AlaudahGeorgia Institute of [email protected]

Muhammad Amir ShafiqGeorgia Institute of TechnologyAtlanta, Georgia, [email protected]

Ghassan AlRegibGeorgia Institute of Technology,Atlanta, Georgia, [email protected]

PP1

Non-Convex Color Image Enhancement Via Mani-fold Regularization

Direct regularization of non-convex image priors pose sev-eral challenges as the energies suffer from multiple min-ima. In this work we introduce a non-convex vectorialtotal variational based method for the problem of colorimage restoration. We exploit a novel intra-channel cou-pling derived from the geometry of an opponent space. Weoptimize our energy using a half-quadratic algorithm and

show that our numerical scheme converge. We show com-petitive results compared to state-of-the-art vectorial totalvariation methods.

Freddie Astrom, Christoph SchnoerrUniversity of [email protected],[email protected]

PP1

A Coupled Regularizer for Color Image Enhance-ment Via Manifold Geometry

Color image enhancement poses an unsettled problem sincethe notion of color edges has no unique characterization.Existing vectorial total variation (VTV) methods have in-sufficient color channel coupling and thus may create colorartifacts. We introduce a novel color channel coupling de-rived from the geometry of an opponent space. We showexistence and uniqueness of a solution in the space of vec-torial functions of bounded variation. Experimentally, weoutperform state-of-the-art VTV methods w.r.t. color con-sistency.

Freddie Astrom, Christoph SchnoerrUniversity of [email protected],[email protected]

PP1

Density Modeling of Images Using a GeneralizedNormalization Transformation

We introduce a parametric nonlinear transformation forjointly Gaussianizing patches of natural images. The trans-formation is differentiable, can be efficiently inverted, andthus induces a density model. It achieves a significantlybetter fit than previous image models, including ICA andradial Gaussianization. Model samples are visually simi-lar to natural image patches. We use the model for imagerestoration, and show that it can be cascaded to build non-linear hierarchies analogous to multiscale representations.

Johannes Balle, Valero LaparraNew York [email protected], [email protected]

Eero P. SimoncelliCourant Institute of Mathematical SciencesNew York [email protected]

PP1

Applications and Generalization of the (p, q)-Laplace Operator

We study and extend a recently proposed family of oper-ators called (p, q)-Laplace operators, which generalize thep-Laplace operator. In this work we have extended the(p, q) operator-class with spatially adaptive p,q coefficients.We present novel preliminary results on the regularity andwell-posedness for the non-adaptive coefficient. We show,via empirical experiments, that our adaptive coefficient op-erator reduces the staircasing effect often seen in total vari-ation whereas we still preserve fine details without loosingimage contrast.

George BaravdishLinkoping University

IS16 Abstracts 145

[email protected]

Freddie AstromUniversity of [email protected]

Yuanji ChengMalmo [email protected]

Olof SvenssonLinkoping [email protected]

PP1

Inverse Reaction-Diffusion Model for TumorSource Localization

Reaction-diffusion models have been successfully used forcancer tumor growth prediction in, e.g., computed tomog-raphy. In this work we study the inverse growth problemwith the aim to locate the tumor origin. We suggest aregularization method posing the inverse problem as a se-quence of well-posed forward problems. Numerical resultsverifies the accuracy of our solution scheme by comparingthe solution from the inverse problem with the correspond-ing synthetic tumor growth from the forward model.

Rym JaroudiENIT-LAMSIN University of Tunis el [email protected]

George BaravdishLinkoping [email protected]

Freddie AstromUniversity of [email protected]

PP1

Connectionist Model of Wavelet Neural Networkin Automatic Pattern Recognition

Inspired by the functioning of the nervous approach, wepropose to build up a wavelet neural network (WNN) ca-pable to identify geometric shapes of an image capturedusing a digital camera. We focus on the exploit of waveletfunctions in the artificial neural network approach. Thedata used to train the WNN are 18 in total; nevertheless,the outcome confirmed the efficiency of the connectionistmodel of wavelet networks in the field of recognition.

Adel BelayadiPreparatory School in Natural and Life Sciences, AlgeriaUniversity of Bab Ezzouar, BP 32, El Alia, 16111, [email protected]

Fawzia Mekideche-ChafaUniversity of Sciences and Technology HouariBoumedieneUSTHB [email protected]

Boualem BourahlaLaboratory of Physics and Quantum Chemistry, M.Mammeri Univ

bourahla [email protected]

PP1

Learning Metrics to Enhance Morphological Cate-gorization

In this presentation, we will present an approach to im-prove morphological categorization by introducing a met-ric learning method that lets us select a shape metric thatoptimizes shape classification among all metrics in a high-dimensional parametric family. To estimate the optimalshape metric, we use a Monte Carlo optimization tech-nique. We will discuss the theoretical and practical aspectsof the method, including applications to the classificationof 3D skull data for several mouse strains. The results ofthis study help validate the proposed method, which in aforthcoming study will be applied to the enhancement ofclinical diagnose of human facial dysmorphic syndromes.

Serdar CellatFlorida State [email protected]

Washington MioDepartment of MathematicsFlorida State [email protected]

Giray OktenFlorida State [email protected]

PP1

3D Shape Characterization of Vascular Remodelingin Pulmonary Arterial Hypertension As Depictedin Volumetric Ct Images

Pulmonary arterial hypertension is a difficult to diagnoseand treat disease where the resistance of the small pul-monary arteries drastically increases resulting in upstreamvascular remodeling. Image-based characterization of thevascular remodeling typically only uses the diameter of thepulmonary arterial trunk. As an alternative, more com-plete characterization, we combine automated graph-basedrecognition of the arterial tree structures with point-based,non-parametric 3D shape models to create a more informa-tive model of the entire vascular remodeling.

Brian E. ChapmanDepartment of RadiologyUniversity of [email protected]

Lynette BrownUniversity of UtahIntermountain [email protected]

John RobertsDepartment of RadiologyUniversity of [email protected]

Tom FletcherDepartment of Computer ScienceUniversity of Utah

146 IS16 Abstracts

[email protected]

PP1

A Unified Hyperelastic Joint Segmenta-tion/registration Model Based on WeightedTotal Variation and Nonlocal Shape Descriptors

In this presentation, we propose a unified variational modelfor joint segmentation and registration in which the shapesto be matched are viewed as hyperelastic materials, andmore precisely, as Saint Venant-Kirchhoff ones. The dis-similarity measure is based on weighted total variationand nonlocal shape descriptors inspired by the Chan-Vese model for segmentation. Theoretical results amongwhich relaxation, existence of minimizers, description andanalysis of a numerical method of resolution, and a Γ-convergence one are provided.

Carole Le Guyader, Noemie DebrouxINSA Rouen, [email protected],[email protected]

Carola-Bibiane SchonliebDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of Cambridge, [email protected]

Luminita A. VeseUniversity of California, Los AngelesDepartment of [email protected]

PP1

A Flexible Approach to 2D-3D Image Registration

We propose an extended mathematical formulation aimedat intensity-based registration (alignment) of a deformed3D volume to a 2D slice as an extension of the existingFAIR (Flexible Algorithms for Image Registration) tool-box. This framework will be evaluated on 2D-3D registra-tion experiments of ”in vivo” cardiac magnetic resonanceimaging (MRI) aimed at computer assisted surgery. Targetregistration error (TRE), Jaccard and Dice indexes will beused to validate the accuracy of the registration scheme onboth simulated and clinical experiments. The approach isflexible and various regularization schemes, similarity mea-sures, and optimization approaches can be considered.

Lorraine Ma, Mehran EbrahimiUniversity of Ontario Institute of [email protected], [email protected]

PP1

A Discretize-Then-Optimize Approach to CoupledSuper-Resolution Reconstruction and Motion Es-timation

The process of recovering a high-resolution (HR) imagefrom a set of distorted (i.e. deformed, blurry, noisy, etc.)low-resolution (LR) images is known as super-resolution.Super-resolution problem will require the reconstruction ofthe ideal HR image and an estimation of the motion be-tween LR images. The proposed algorithm will attemptto recover the HR image and perform non-parametric mo-tion estimation simultaneously using a joint regularized ill-posed inverse model followed by a discretize-then-optimize

approach. Elastic regularization will be used for non-parametric motion estimation and total variation regular-ization for the super-resolved image. Preliminary resultson surveillance image sequences will be presented.

Eric Ng, Mehran EbrahimiUniversity of Ontario Institute of [email protected], [email protected]

PP1

On the Asymptotic Optimality of Global Image De-noising

In this work, we focus on the global denoising frameworkrecently introduced by Talebi & Milanfar and analyze theasymptotic behavior of its RMSE restoration performancewhen the image size tends to infinity. We introduce preciseconditions both on the image and the global filter to ensureand quantify this convergence. We also discuss open issuesconcerning the most challenging aspect, namely optimalchoice of basis.

Antoine Houdard, Andres AlmansaLTCI CNRS Telecom [email protected],[email protected]

Julie DelonUniversite Paris [email protected]

PP1

Radial Symmetric Point Spread Estimation andUncertainty Quantification

Image deblurring techniques derived from convolution re-quire, a priori, an estimate for the convolution kernel orpoint spread function (PSF). Standard techniques for es-timating the PSF involve imaging a bright point source,but this is not always feasible (e.g. high energy radiogra-phy). We present a method for estimating and quantifyinguncertainty that is suitable for applications where it is pos-sible to image a sharp edge which requires an assumptionof radial symmetry. Taking a Bayesian approach, we de-velop a Hilbert space that generalizes radial symmetry forour prior, and, using a novel marginalized Gibbs samplingalgorithm, we compute a Monte Carlo estimate of the pos-terior distribution of the PSF.

Kevin JoyceUniversity of MontanaDepartment of Mathematical [email protected]

PP1

Applying Local Renyi Entropy to Enhance ElectronMicroscopy Images of the Nucleus

Local Renyi and Shannon entropy, have proven to be verypowerful in image processing. Examples include, auto-mated image quality measures, contouring, noise reduc-tion and thresholding for object detection and segmenta-tion performed on various images including biological. Wedemonstrate applying Renyi entropy for enhancing Elec-tron Microscopy images of the cell nucleus. These resultsmay be used in EM tomography to obtain 3D structuresof the cell nucleus which relate to how DNA information is

IS16 Abstracts 147

being accessed.

Tsvi KatchalskiResearch Fellow, NCMIR, [email protected]

Albert LawrenceNCMIR, [email protected]

Mark EllismanUniversity of California, San [email protected]

PP1

Extracting Science from the Smallest Scales in So-lar Imagery

All digital images are corrupted by noise. In most solarimaging, we have the luxury of high photon counts andlow background contamination, which when combined withcarful calibration, minimize much of the impact noise hason the measurement. Outside high-intensity regions, suchas in coronal holes, the noise component can become sig-nificant and complicate feature recognition and segmenta-tion. We create a practical estimate of noise in the high-resolution solar images across the detector CCD. A mixtureof Poisson and Gaussian noise is well suited in the digitalimaging environment due to the statistical distributions ofphotons and the characteristics of the CCD. Using state-of-the-art noise estimation techniques, the publicly availablesolar images, and point spread function estimates; we con-struct a maximum-a-posteriori assessment of the error inthese images. The estimation and mitigation of noise notonly provides a clearer view of solar features in the solarcorona, but also provides a peek into the smallest physicalscales observed on the sun.

Michael S. Kirk, C. Alex Young, W. Dean PesnellNASA Goddard Space Flight [email protected], [email protected],[email protected]

PP1

Restoration of Compressed Noisy Images

A noisy image f+n, where f denotes the original scene andn the additive noise is compressed. In order to restore f ,we model the noise corrupting the compressed ideal image.It is typically sparse in the transformed domain used forthe compression. We then propose a model for restoring fand describe a numerical scheme solving this model. Wefinally study the performances of the model.

Francois MalgouyresInstitut de Mathematiques de ToulouseUniversite Paul [email protected]

Thomas OberlinUniversity of [email protected]

Herwig WendtIRIT

[email protected]

PP1

Models and Algorithms for 3D Corneal Biometryfrom Optical Coherence Tomography

Optical coherence tomography (OCT) is a noninvasivehigh resolution medical imaging modality based on near-infrared interferometry. Already a popular tool in ophthal-mology, OCT has the potential to uncover detailed infor-mation about the interior of the eye that is unavailablethrough current technology. This presentation will addresskey issues involved in accurate reconstruction of the corneafrom OCT data, including automatic outlier removal andimage registration, data interpolation, and refraction cor-rection for interior ocular surfaces.

Micaela Mendlow, Mansoor HaiderNorth Carolina State [email protected], [email protected]

Eric BucklandLeica [email protected]

PP1

High-Level Fusion for Multimodal Brain Imag-ing Data Using Conditional Probabilities and Di-rected Information Flow Between Clustered Fea-ture Spaces

We introduce an intuitive high-level multimodal data fu-sion framework based on Markov-style flows in an ambient”meta-space” of diverse features. Our approach quanti-fies directed information transfer between clinically rele-vant features of arbitrary type or dimensionality. We applythe framework in a large fMRI dataset to identify relation-ships between 4D spectrum, functional network connectiv-ity, connectivity dynamism and schizophrenia.

Robyn MillerThe Mind Research [email protected]

Vince CalhounThe University of New [email protected]

PP1

Stability of Information Theoretic K-Space Trajec-tories for Model-Based MR Thermal Image Recon-struction

An information theoretic analysis is presented to evaluatethe stability of the most information-rich k-space trajec-tories in model-based magnetic resonance (MR) thermalimage reconstruction. Novel Gauss-Hermite quadratureschemes were developed to compute mutual informationbetween a nonlinear model-based image reconstruction andMR signal measurements. The stability of the most infor-mative k-space samples is compared in several treatmentscenarios for MR-guided laser induced thermal therapy inheterogeneous human brain tissue.

Drew Mitchell, Reza Madankan, Samuel Fahrenholtz,Christopher MacLellan, Wolfgang StefanUniversity of Texas MD Anderson Cancer [email protected], [email protected],

148 IS16 Abstracts

[email protected],[email protected], [email protected]

Jason StaffordMD Anderson Cancer [email protected]

John Hazle, David FuentesUniversity of Texas MD Anderson Cancer [email protected], [email protected]

PP1

A Stochastic Inverse Method for Highly Heteroge-neous Aquifers

Aquifer properties such as permeability are often highlyheterogeneous with significant variations occurring on thecentimeter scale and sometimes smaller. For many hy-drogeologic applications, an attempt is made to infer theaquifer properties by observing the aquifer’s response tostimulation (e.g., pumping, tracer injection, etc.) at a num-ber of monitoring wells that are sparsely distributed acrossa field whose length scale is often tens, hundreds, or thou-sands of meters. This disparity in scales makes it difficult,and perhaps impossible, for inverse methods to reproducethe small scale heterogeneities that are present in the ac-tual aquifer. Most inverse methods that are in use producefields (e.g., permeability fields) that are much smootherthan we expect the actual field to be, essentially failing torepresent the small scale heterogeneity at all. This failureis important because small scale heterogeneities can havea significant impact on transport (e.g., trapping in small,low-permeability lenses). We present an approach to in-verse analysis that is capable of representing these smallscale heterogeneities. We note that although this approachdoes represent small scale heterogeneities, it does not re-produce the actual small scale heterogeneities that existin the aquifer. The representation of the small scale het-erogeneities is stochastic, and, because of this, we call themethod a stochastic inverse method.

Daniel O’MalleyComputational Earth ScienceLos Alamos National [email protected]

PP1

Enhanced Low-Rank Matrix Approximation

We propose to estimate low-rank matrices by formulat-ing a convex optimization problem with non-convex reg-ularization. We employ parameterized non-convex penaltyfunctions in order to estimate the non-zero singular valuesmore accurately than the nuclear norm. We further pro-vide a closed form solution for the global optimum of theproposed objective function (sum of data fidelity and thenon-convex regularizer). The closed form solution reducesto the singular value thresholding method as a special case.

Ankit ParekhDepartment of Mathematics, School of EngineeringNew York [email protected]

Ivan SelesnickDepartment of Electrical and Comp. EnggNYU School of Engineering

[email protected]

PP1

Efficient Optimal Recovery Based Spatially-Adaptive Multi-Frame Super-Resolution.

Our approach to multi-frame super-resolution based on theframework of optimal recovery was recently extended to aspatially-adaptive scheme whereby the block-by-block pro-cessing is modified based on local low-resolution image datausing simple statistical quantities to define local bandwidthfor the high-resolution image block. Simulations show thesuperiority of the adaptive scheme over other methods thatare computationally fast. Our current work is focused onimproving this approach based on: pre-optimized but fixedregularization parameter, automated linking of the blockvariances to the bandwidth parameter, incorporation ofgradients and edge maps, and post-processing using de-blocking.

Sergio D. Cabrera, Luis PonceUniversity of Texas at El [email protected], [email protected]

PP1

Color Image Processing By Vectorial Total Varia-tion With Gradient Channels Coupling

We study a regularization method for multichannel imagesbased on the vectorial total variation approach along withchannel coupling for color image processing, which facili-tates the modeling of inter channel relations in multidimen-sional image data. We focus on penalizing channel gradi-ent magnitude similarities by using L2 differences, whichallow us to explicitly couple all the channels along witha vectorial total variation regularization for edge preserv-ing smoothing of multichannel images. By using matchedgradients to align edges from different channels we obtainmultichannel edge preserving smoothing and decomposi-tion. A detailed mathematical analysis of the vectorial to-tal variation with penalized gradient channels coupling isprovided. Extensive experimental are given to show thatour approach provides good decomposition and denoisingresults in natural images. Comparison with previous colorimage decomposition and denoising methods demonstratethe advantages of our approach.

Surya PrasathUniversity of [email protected]

Juan C. MorenoUniversity of Beira Interior, [email protected]

PP1

Whitening of the Residual for Image Denoising

Most state-of-the-art denoising methods that rely on awhite gaussian noise hypothesis do not guarantee thewhiteness of the method-noise (residual between the noisyimage and the estimated image). Typically, the areaswhere the method-noise is correlated convey wrong in-formation. We propose a new variational approach withan energy defined to guarantee the local whiteness ofthe method-noise and ensure information conservation. Itleads to applications such as denoising, performance eval-

IS16 Abstracts 149

uation, post-processing or multi-image denoising.

Paul H. Riot, Yann GousseauTelecom [email protected], [email protected]

Florence TupinTELECOM ParisTech, Paris (France)[email protected]

Andres AlmansaTelecom [email protected]¿

PP1

Denoising of Images Using Redundant WaveletTransform and Biorthogonal Slepian Filterbanks

The redundant discrete wavelet transform (RDWT) wasoriginally developed as an approximation to the continu-ous wavelet transform by removing the downsampling op-eration from the critically sampled discrete wavelet trans-form. In this work, we analyze the performance of RDWTfor image denoising under additive noise when the RDWTis implemented using biorthogonal filters rather than or-thonormal filters. The filters to be used are derived fromSlepian sequences which are the eigenfunctions of an energymaximization problem.

Seda SenayNew Mexico Institute of Mining and [email protected]

PP1

Multiphase Segmentation For Simultaneously Ho-mogeneous + Textural Images

In their seminal paper from 1989, Mumford and Shahproposed a model (but NP-hard due to the Hausdorff 1-dimensional measure H1 in R2) for piece-wise smooth (forimage restoration) and piece-wise constant (for image seg-mentation) by minimizing the energy functional. Later,Chan and Vese have proposed the active contour model fortwo phase image segmentation which is solved by a levelset method. However, these models do not apply to thelarger class of natural images that simultaneously containstexture and piecewise smooth information. By the calculusof variation, we design a bi-level constrained minimizationmodel for a simultaneous multiphase homogeneous and tex-tural (on a defined scale) image segmentation by solving arelaxed version of a non-convex (due to a binary settingof a non-convex set) minimization. The cornerstone of thisminimization is to introduce novel norms which are definedin different functional Banach spaces (with the discrete set-ting), e.g. homogeneous regions, texture and residual aremeasured by directional total variation norm, directionalG-norm and a dual of a generalized version of the Besovspace, respectively. The key ingredients of this study are:(1) the assumption of the sparsity of a signal in some trans-form domains; (2) the Banach space G in Meyer’s model tomeasure the oscillatory components e.g. texture, which donot have a small norm in L1(R2) or L2(R2); (3) a smoothsurface and sharp edges in geometric objects in cartoonalong with a smooth and sparse texture by the DG3PDmodel.

Duy H. ThaiStatistical and Applied Mathematical Science Institute

[email protected]

PP1

Imaging of Contaminant Plumes Using Non-Nonnegative-Matrix Factorization

Contamination of groundwater water-supply resourcesposes significant social and environmental problems. Fre-quently, at the contamination sites, the groundwater is amixture of waters with different origins (sources) that arecommingled in the aquifer; several of these groundwaterrecharge sources might include contaminants. Typically,all these sources will have different geochemical signaturesdue to differences in their origins and flowpaths through thesubsurface before infiltrating in the aquifer. The identifica-tion of the contamination/infiltration sources causing theobserved geochemical concentrations in the aquifer can bevery challenging at sites where complex physical and chem-ical processes occur. We propose mapping of the contami-nant plumes based on a novel model-free machine-learningalgorithm.

Velimir V. VesselinovLos Alamos National [email protected]

IS16 Abstracts64 IS16 Abstracts IP1 Nonconformist Image Processing with the Graph Laplacian Operator...

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