Post on 25-Aug-2020
Méthodes d’imagerie pour les écoulements et le CND
Journée scientifique FED3G
CEA LIST/Lab Imagerie Tomographie et Traitement
Samuel Legoupil
15 juin 2012
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2D/3D imaging tomography Example
Petrochemical reactor scanner :
Liquid distribution in
a fixed bed reactor
(3 hydrodynamics
conditions)
µtomography imaging :
3D-Fuel injector Ni foam for gas distributor
and 3D image analysis results
Carbon GDL
For fuel cell (fiber=5µm)l
Menisci shape in
A 100x20 µm canal
For microfluidics XPIV for flow
characterization
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Context
Basics of CT and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implémentation and adaptative data representation
Future developments
Outline
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Introduction
• Tomographic Imaging Reconstruction with Non-diffracting Sources
• Tomographic Imaging with Diffracting Sources
• Reflection Tomography
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Tomography under progress
Number of papers with “x-ray” and “CT”,
From Ge Wang - Med. Phys. 35, March 2008
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Differences between medical and industrial imaging
Medical Industrial
Sample
dimensions =0.75 x L=2 m² 10-3 3m
Sample dynamics 0 50 Hz 0 10 kHz
Dose As low as possible No constraint
Processing time Short No constraint
Contrast 1% 1%
Sampling
conditions Good
Weak most oftenly –
partial view of object
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Context
Growing-up of X-ray CT controls as a standard tool:
Material science, biology,
Earth science, archeology…
CT integration for on-line control of manufactured objects
turbine blades,
medicine industry for spray dispenser
High complexity of the method
Tedious experimental optimization
© NIKON
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Context
Basics and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implementation and adaptative data representation
Future developments
Outline
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CT General principles Physics
Absorption of media, depends on :
• Material characteristics (Z density, density, thickness)
• Photon energy
The optimal energy for the measurement must satisfy :
E
d
dEeI
I )(
0
dE
2)(
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CT General principles Optimal energy
0.1
1
10
100
0 10 20 30 40 50
Energy (keV)
Ab
so
rpti
on
co
eff
icie
nt
(cm
²/g
)
µ - Xcom (cm²/g)
µ - Fit (Power)
dE
cE )(
keVE 405
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CT General principles Optimal energy
E d d
E
2
)(
0
0.2
0.4
0.6
0.8
1
1.2
0 15 30 45 60 75 90 105 120 135 150 165 180
Projection angle
Sam
ple
th
ickn
ess d
(cm
)
0
2
4
6
8
10
12
14
16
18
Op
tim
al en
erg
y (
keV
)
0.01
0.1
1
10
100
0 15 30 45 60 75 90 105 120 135 150 165 180
Projection angle
Rela
tive e
rro
r o
n m
easu
rem
en
t
E=6keV
E=16keV
E=11keV
R=a/b=10
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Constraints on acquisition
Projection configurations
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Constraints on object
Object configuration
Partial view of the object Complex support of reconstruction
domain
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Context
Basics and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implementation and adaptative data representation
Future developments
Outline
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Iterative Algorithms
For example, ML-EM, OS-EM, ART, GC, …
Discretize the image into pixels
Solve imaging equations AX=P
X = unknowns (pixel values)
P = projection data
A = imaging system matrix
P
X
aij
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Iterative Algorithms Regularisation - example
)()(1 2
2 jiii
i i
xxVpXAF
V
If V(x) = x2, it enforces smoothness.
Data matching Noise model
Prior
encouragement
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Inversion methods Statistical approach
Problem description in Emission Tomography
Problem description in Transmission Tomography (CT)
• Estimation of H
• Law of noise
• Choice of approach and associated algorithm(s)
• Iterative method :
• Statistical inversion :
)|(maxargˆ fgPf x
)()|(maxargˆ fPfgPf x
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Projection matrix in algebraic approaches
Reconstruction model
dEdxExµEII )),(exp()(
)exp(0 µdxII
AµAµI
Iy i
jj 0ln
i
Voxel
x y
z
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Projection matrix in algebraic approaches
yj
aij
Source
Projection (A):
i
iijj ay
Backprojection (AT):
j
jiji ya
2AµyJ
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Photons scattering in cone beam CT
Evolution of build-up (1+Nscattered photons/Ndirect photons )
Dsource-object=50 mm
Dsource-detector=200 mm
Det. size=100 mm
U=160 kV
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Projection matrix in algebraic approaches
yj
aij
Source
ai’j
Projection (A):
Backprojection (AT):
2AµyJ
Distance to beam axis
i
iijj ay
j
jiji ya
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Projection matrix in algebraic approaches
Example of weighted function calculated with CIVA
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Context
Basics and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implementation and adaptative data representation
Future developments
Outline
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Reconstruction from few projections
The objective is the reconstruction from few X-ray projections:
Speed-up of acquisition process
Low-dose for medical imaging
The inverse problem is highly ill-posed need for specific approach
Reconstruction by
analytic inversion Frequential domain
projections (11 proj.) Original object
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Reconstruction from few projections
Recent developed Compressed sensing theory confirms that with a
sampling rate lower than the Nyquist rate, we can also perfectly
reconstruct a signal.
- Sparse representation of signal under appropriate basis
(sinusoid, wavelet…)
- Reconstruction solving a convex optimization problem.
21
..min bAxtsxx
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Reconstruction from few projections
As images are rarely sparse, the idea is to find a transform α=(µ)
such that the transformed coefficients are sparse, eg Total
Variation of µ:
2
*
1..min bAts
Compressed
sensing
Reconstruction by
analytical inversion Original object
1
0
1
0
2
,
2
,)(N
i
N
j
jiyjixTV
*
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Methods comparison
Reconstruction from 32 projections
FBP OS-EM Comp. Sensing
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Context
Basics and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implementation and adaptative data representation
Future developments
Outline
■ 29
Computer implementation
Computer implementation has to estimate
Hfg gHf Tand
2D detector=N² pixels
Reconstruction
Volume = N3 voxels
Np projections
Matrix H sizes NpxN2xN
(non-null elements)
N Np GBytes
256 64 2
512 256 64
1024 512 1024
2048 512 8192
GPU
hardware
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Example: Ni foam drying
ART Bayesian approach
Speed-up factors:
• x 240 on projection
• x 80 on back projection
Reconstruction volumes :
• 10243
• 20483
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Adaptative information representation
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Adaptative information representation
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CIVA NDT Platform – CT module
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2D knee reconstruction
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Context
Basics and industrial constraints
Projection matrix and modeling needs
CS reconstruction methods
Implementation and adaptative data representation
Future developments
Outline
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Instantenous imaging
2 juillet 2008
Synchronous phenomenon
Relevant information
Pompe axis
Multi sources
Multi sensors
Asynchronous phenomenon
max=25%
max=39%
max=44%
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Nouvelles technologies de sources X
2 juillet 2008
Avantages des sources à base de CNT :
– Fort courant (100 µA/tube)
– Source nano-foyer
• Très haute résolution spatiale
• Imagerie par contraste de phase
– Source étendue
• Haute intensité
• Codage de source
– Sources multiples
• Tomographie dynamique
Voir http://www.nanosprint.com/index.php?id=94
D. Pribat
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Simulation of robot CT
Local imaging on a « C3 » :
• conformity assessment
• Defect detection
• Competition analysis
Reconstructed « middle foot »
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CIVA-RT / CIVA-CT Platform for NDT evaluation (US, CF and X-ray)
CIVA RX
Plug-in
Tomo
GUI Tomo
Civa
visualisation
Analytical
algo
Algebraic
algo
Statistical
algo
High
performance
calculation
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Future developments
Data
Processing
Sensors
Industrial
situation
Data
acquisition
Modeling Information
• Hardware developments
• X-ray detector: fine resolution, dynamic, multi energy
• X-ray generator: microfocus source (@ 200 nm), adaptative, c
• Modeling capacities (from physics to signal theory) and reconstruction
• Database reconstruction
• Computation capacities (GPU hardware, Larabi…)
• Information processing
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