méthodes d’imagerie pour les écoulements et le cnd · méthodes d’imagerie pour les...

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

http://www.enterprise-europe-network.ec.europa.eu/src/request/pictures/Alufelge.jpg

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Context

Basics and industrial constraints



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





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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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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yj

aij

Source

ai’j

Projection (A):

Backprojection (AT):

2AµyJ

Distance to beam axis

i

iijj ay

j

jiji ya

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Example of weighted function calculated with CIVA

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Context





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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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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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





Future developments

Outline

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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





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

http://www.nanosprint.com/index.php?id=94

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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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