Physics-Based Signal and Image ProcessingPhysics-Based Signal and Image Processing

Prof. Eric Miller, Dr. Basak Ulker KarbeyazDept. of Electrical and Computer Engineering

Northeastern Universityelmiller@ece.neu.eduProf. Robin Cleveland

Dept. Mechanical and Aeronautical Eng.Boston UniversityRobinc@bu.edu

Prof. Eric Miller, Dr. Basak Ulker KarbeyazDept. of Electrical and Computer Engineering

Northeastern Universityelmiller@ece.neu.eduProf. Robin Cleveland

Dept. Mechanical and Aeronautical Eng.Boston UniversityRobinc@bu.edu

OverviewOverview

Introduction to physics-based signal and image processingOverview of research projects and collaboratorsRepresentative effort

Quantitative ultrasound imaging for guidance of cancer treatment

Future work

Introduction to physics-based signal and image processingOverview of research projects and collaboratorsRepresentative effort

Quantitative ultrasound imaging for guidance of cancer treatment

Future work

Physics Based Signal ProcessingPhysics Based Signal Processing

Goal: extract information regarding internal structure

ImageObjects: what & where

Data from transducers on the boundary

Time or frequency domainProblems

Sparse noisy dataLimited apertureCluttered backgroundComplicated mapping from unknowns to data

ApplicationsUltrasoundDiffuse optical tomographyResistance tomography

Goal: extract information regarding internal structure

ImageObjects: what & where

Data from transducers on the boundary

Time or frequency domainProblems

Sparse noisy dataLimited apertureCluttered backgroundComplicated mapping from unknowns to data

ApplicationsUltrasoundDiffuse optical tomographyResistance tomography

The FrameworkThe Framework

Computational sensormodels

Experimentallaboratory facilities

Informationextraction methods

Our strengthsWhere we look for collaboration

CollaborationCollaboration

Wide variety of institutionsOther universities (BU, Ole Miss, U Toronto)Industry (Textron, BAE/Alphatech, Coherent)Hospitals (MGH, BWH)Gov’t labs (INL)

Wide variety of ways we work togetherA place for my students to immerse themselves in the problemIntellectual exchange (problem statements, data, models)Joint proposalsFunding

Wide variety of institutionsOther universities (BU, Ole Miss, U Toronto)Industry (Textron, BAE/Alphatech, Coherent)Hospitals (MGH, BWH)Gov’t labs (INL)

Wide variety of ways we work togetherA place for my students to immerse themselves in the problemIntellectual exchange (problem statements, data, models)Joint proposalsFunding

Geometric Imaging MethodsGeometric Imaging Methods

Discrete “objects” against (possibly) inhomogeneous backgroundMany examples

Defects/crack in NDETumors in medical imagingTreated regions in image guided surgeryAreas of functional brain activityPollution plumes in environmental remediation

Discrete “objects” against (possibly) inhomogeneous backgroundMany examples

Defects/crack in NDETumors in medical imagingTreated regions in image guided surgeryAreas of functional brain activityPollution plumes in environmental remediation

Geometric Methods (cont)Geometric Methods (cont)

Option 1Estimate many, many pixels and then “segment” out objectsMany difficulties if a priori you have an “object” problem

Option 2Use data to determine size, shape, perhaps number, and contrast of objects as well as something about backgroundFar fewer geometric unknowns than pixelsBetter adapted to underlying problem

Option 1Estimate many, many pixels and then “segment” out objectsMany difficulties if a priori you have an “object” problem

Option 2Use data to determine size, shape, perhaps number, and contrast of objects as well as something about backgroundFar fewer geometric unknowns than pixelsBetter adapted to underlying problem

UltrasoundUltrasound

Medical imaging & nondestructive evaluation (NDE)Scan transmitter and receiverBuild up an image of

“Reflectivity”Sound speedDensityAbsorption

Time-of-flight pretty easyMore sophisticated methods not so simple

Medical imaging & nondestructive evaluation (NDE)Scan transmitter and receiverBuild up an image of

“Reflectivity”Sound speedDensityAbsorption

Time-of-flight pretty easyMore sophisticated methods not so simple

Skin

Fig. 0.1. Focused Ultrasound Surgery.

Ultrasound lesionUltrasoundtransducer

Target organ

Thanks to Prof. Ron Roy of BU

An Ultrasound ProblemAn Ultrasound Problem

• Ultrasonic image guided cancer treatmentapplication

• High intensity focused ultrasound (HIFU) transducer heats and kills tissue

• Necrosis causes changes in tissue properties: sound speed, attenuation, and maybe density

• Each focal area is small compared to the tumor and cigar shaped

• Can we use ultrasound (as opposed to MRI) to monitor treatment?

• Conventional image formation not adequate

• Brute force inverse scattering approachnot feasible

• Exploit prior information to obtain tractable solution

Problem FormulationProblem Formulation

The pressure signal scattered from an inhomegenity of sound speed attenuation and density in homogenous medium is given by:

Lossy, homogenous background.Contrast of the scatterer is weak. BORN Approximation is valid.

The pressure signal scattered from an inhomegenity of sound speed attenuation and density in homogenous medium is given by:

Lossy, homogenous background.Contrast of the scatterer is weak. BORN Approximation is valid.

ps (r,ω ) = − ks2 (ro,ω )G(r,ro,kb (ω ))

V '∫ pb (r,ro,kb (ω ))d 3ro

− σ p (ro )V '∫ ∇G(r,ro,kb (ω ))•∇pb (r,ro,kb (ω ))d 3ro

Density: σ p = ln 1+ρp (r)ρb

⎛

⎝⎜⎞

⎠⎟ks

2 = cp (r) −2ω 2

cb3

⎡

⎣⎢

⎤

⎦⎥ +α p (r,ω ) − j

2ωcb

⎡

⎣⎢

⎤

⎦⎥

kb2 =

ω 2

cb2

⎡

⎣⎢

⎤

⎦⎥ − j

2ωαb (ω )cb

⎡

⎣⎢

⎤

⎦⎥

Cylindrical TransducerCylindrical Transducer

Integral can not be solved analytically.It is oscillatory and numerical integration is not attractiveApproximation procedure:

Change integral from from dz to drExploit smallness of φDo φ integral first (analytically)Project slowly varying r integral onto Legendre basisIntegrate expansion analytically

Details depend on observation point where data are collectedThe computation time is 0.3 seconds in Matlab per observation point as opposed to 3 hours using numerical techniques.Validated with experimental data

Integral can not be solved analytically.It is oscillatory and numerical integration is not attractiveApproximation procedure:

Change integral from from dz to drExploit smallness of φDo φ integral first (analytically)Project slowly varying r integral onto Legendre basisIntegrate expansion analytically

Details depend on observation point where data are collectedThe computation time is 0.3 seconds in Matlab per observation point as opposed to 3 hours using numerical techniques.Validated with experimental data

φb (rp ) =R

4πe− jk (rp cos(φp )−R cos(φ ))2 +(rp sin(φp )−R sin(φ ))2 +(zp − z )2

(rp cos(φp )−R cos(φ ))2 +(rp sin(φp )−R sin(φ ))2 +(zp − z )2S∫ dφdz

Object ModelObject Model

Model treatment region as an ellipsoid

Linearized physical model (significant effort modeling real transducers)Estimate ellipsoid parameters from data

Model treatment region as an ellipsoid

Linearized physical model (significant effort modeling real transducers)Estimate ellipsoid parameters from data

DUT (r − c)2

2≤ 1

c = xo, yo, zo[ ]TD = diag(1 a ,1 b,1 c)U = F(θ1,θ2 ,θ3)

ab

(xo , yo , zo )

Object Model (2)Object Model (2)Formally, the contrast function for an ellipsoidal perturbation is defined as

Step is not smooth and we would like to use a gradient-dent type method for parameter estimation. Employ smooth version of step function

Formally, the contrast function for an ellipsoidal perturbation is defined as

Step is not smooth and we would like to use a gradient-dent type method for parameter estimation. Employ smooth version of step function

cp r( )= cpu 1− DUT (r − c)2

2( ) u x( )=1 x ≥ 00 else⎧⎨⎩

cp r( )= exp(Msech(α DUT (r − c)2

16)) −1

exp(M) −1

ProcessingProcessing

One ellipse for each physical property:Sound speedAttenuationDensity

Model is nonlinear in ellipsoid parameters but differentiableUse Gauss-Newton method to estimate parameters from data assuming least-squares cost function (Gaussian noise)

One ellipse for each physical property:Sound speedAttenuationDensity

Model is nonlinear in ellipsoid parameters but differentiableUse Gauss-Newton method to estimate parameters from data assuming least-squares cost function (Gaussian noise)

Numerical ExperimentNumerical Experiment

• Linear array of 5 point sources• ROI is 5mm x 5mm x 5 mm

(16 x 16 x 16)• 6 frequencies between 300

kHz-425kHz.• Array scanned across aperture

(6 measurement points)• Homogeneous, lossy

background • Power law attenuation• Homogeneous sound speed,

density and attenuation anomaly

• Unknown contrasts • 25dB SNR • cb = 1551 m/s, αbo =3.6 Np/m,• ρb=1045 kg/m3

ResultsResults

cp= 3.5m/s αpo= 3.5 Np/m

Estimated Speed

True

Estimated Density

ρp= 5 kg/m3

Estimated Attenuation

Initial guess

Real Data ResultsReal Data Results((Bovine Serum Albumin) BSA PhantomBovine Serum Albumin) BSA Phantom

Enhanced ImagePhotograph of the BSA Phantom

H= 125 mm

R=65 mm

z

x

ResultsResults

cp= 5m/scp= 20m/sαpo= 440 Np/m

cp= 5.8m/sαpo= 46.34 Np/m αpo= 48.7 Np/m

Initial Estimate True

Future Opportunities:Driving ApplicationsFuture Opportunities:Driving Applications

Medical Bio-optical: Cancer screening, brain imaging, molecular imaging, microscopy, …Acoustic: continuation of ultrasound work

EnvironmentalUnexploded ordnanceMonitor and control of the fate and transport of species moving through the underground

Homeland SecurityExplosives detection, baggage inspection, …

Medical Bio-optical: Cancer screening, brain imaging, molecular imaging, microscopy, …Acoustic: continuation of ultrasound work

EnvironmentalUnexploded ordnanceMonitor and control of the fate and transport of species moving through the underground

Homeland SecurityExplosives detection, baggage inspection, …

Future Opportunities:Technical IssuesFuture Opportunities:Technical Issues

Non-trivial multi-sensor processing for single, coherent characterization of the mediumNew physical models (e.g. flow and transport)Imaging over space and timeNew methods for characterizing shapeIntegration of experiment and theory

Non-trivial multi-sensor processing for single, coherent characterization of the mediumNew physical models (e.g. flow and transport)Imaging over space and timeNew methods for characterizing shapeIntegration of experiment and theory

Future Opportunities:Teaming and CollaborationFuture Opportunities:Teaming and Collaboration

Success in the present (and likely future) funding environment requires real collaborationTeams of people with expertise in

Analytics ExperimentsComputationDriving applications

Drawn from academia, industry, and government labsExist opportunities out there (NSF, NIH, DoD) for well-seeded groups to succeed in acquisition of large scale, long term, interesting research funding

Success in the present (and likely future) funding environment requires real collaborationTeams of people with expertise in

Analytics ExperimentsComputationDriving applications

Drawn from academia, industry, and government labsExist opportunities out there (NSF, NIH, DoD) for well-seeded groups to succeed in acquisition of large scale, long term, interesting research funding