Méthodes d imagerie pour les écoulements et le CND Journée scientifique FED3G CEA LIST/Lab Imagerie Tomographie et Traitement Samuel Legoupil 15 juin 2012
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 2
Outline Context Basics of CT and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implémentation and adaptative data representation Future developments 3
Introduction Tomographic Imaging Reconstruction with Non-diffracting Sources Tomographic Imaging with Diffracting Sources Reflection Tomography 4
Tomography under progress Number of papers with x-ray and CT, From Ge Wang - Med. Phys. 35, March 2008 5
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 6
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 7
Outline Context Basics and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implementation and adaptative data representation Future developments 8
CT General principles Physics Absorption of media, depends on : Material characteristics (Z density, density, thickness) Photon energy E I I 0 e ( E) d d The optimal energy for the measurement must satisfy : ( E) 2 d 9
Absorption coefficient (cm²/g) CT General principles Optimal energy 100 µ - Xcom (cm²/g) ( E) c E d 10 µ - Fit (Power) 5 E 40keV 1 0.1 0 10 20 30 40 50 Energy (kev) 10
Sample thickness d (cm) Optimal energy (kev) Relative error on measurement CT General principles Optimal energy E d ( E) 2 d 1.2 1 0.8 R=a/b=10 18 16 14 12 100 10 E=6keV E=16keV E=11keV 10 0.6 8 1 0.4 6 4 0.1 0.2 2 0 0 0 15 30 45 60 75 90 105 120 135 150 165 180 Projection angle 0.01 0 15 30 45 60 75 90 105 120 135 150 165 180 Projection angle 11
Constraints on acquisition Projection configurations 12
Constraints on object Object configuration Partial view of the object Complex support of reconstruction domain 13
Outline Context Basics and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implementation and adaptative data representation Future developments 14
Iterative Algorithms For example, ML-EM, OS-EM, ART, GC, Discretize the image into pixels Solve imaging equations AX=P P X = unknowns (pixel values) P = projection data A = imaging system matrix a ij X 15
Iterative Algorithms Regularisation - example Noise model Data matching Prior encouragement V F i 1 2 ( A ) ( 2 i X pi V x i i x j ) If V(x) = x 2, it enforces smoothness. 16
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 : fˆ fˆ arg max x arg max P( g x f ) P( g f ) P( f ) 17
Projection matrix in algebraic approaches Reconstruction model I I( E)exp( µ ( x, E) dx) de I I 0 exp( µdx) i Voxel y ln I I 0 µ j A i j Aµ z y x 18
Projection matrix in algebraic approaches y j J y Aµ 2 a ij Projection (A): y j a ij i Backprojection (A T ): i j a ij y i j Source 19
Photons scattering in cone beam CT Evolution of build-up (1+N scattered photons /N direct photons ) D source-object =50 mm D source-detector =200 mm Det. size=100 mm U=160 kv 20
Projection matrix in algebraic approaches y j J y Aµ 2 a ij Projection (A): y j a ij i i a i j Distance to beam axis Backprojection (A T ): i j a ij y j Source 21
Projection matrix in algebraic approaches Example of weighted function calculated with CIVA 22
Outline Context Basics and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implementation and adaptative data representation Future developments 23
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 Original object Frequential domain projections (11 proj.) Reconstruction by analytic inversion 24
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. min x x 1 s. t. Ax b 2 25
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: TV( ) N 1 N 1 i0 j0 x 2 i, j y 2 i, j min s. t. 1 * A b 2 * Original object Reconstruction by analytical inversion Compressed sensing 26
Methods comparison Reconstruction from 32 projections FBP OS-EM Comp. Sensing 27
Outline Context Basics and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implementation and adaptative data representation Future developments 28
Computer implementation Computer implementation has to estimate g Hf and f H T g Reconstruction Volume = N 3 voxels 2D detector=n² pixels N p projections Matrix H sizes N p xn 2 xn (non-null elements) N N p GBytes 256 64 2 512 256 64 1024 512 1024 2048 512 8192 GPU hardware 29
Example: Ni foam drying ART Bayesian approach Speed-up factors: x 240 on projection x 80 on back projection Reconstruction volumes : 1024 3 2048 3 31
Adaptative information representation 32
Adaptative information representation 33
CIVA NDT Platform CT module 34
2D knee reconstruction 35
Outline Context Basics and industrial constraints Projection matrix and modeling needs CS reconstruction methods Implementation and adaptative data representation Future developments 36
Instantenous imaging Synchronous phenomenon Asynchronous phenomenon max =25% Pompe axis max =39% Relevant information max =44% Multi sources Multi sensors 2 juillet 2008 37
Nouvelles technologies de sources X 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 D. Pribat Voir http://www.nanosprint.com/index.php?id= 2 juillet 2008 38
Simulation of robot CT Local imaging on a «C3» : conformity assessment Defect detection Competition analysis Reconstructed «middle foot 40
CIVA-RT / CIVA-CT Platform for NDT evaluation (US, CF and X-ray) GUI Tomo Analytical algo CIVA RX Civa visualisation Plug-in Tomo Algebraic algo Statistical algo High performance calculation 41
Future developments Industrial situation Modeling Data Processing Information Sensors Data acquisition 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 42
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