J. Ripoll, Crete 2010 Partner 3: FORTH Contribution Fast Inversion Methods (WP3) Jorge Ripoll,...

J. Ripoll, Crete 2010

Partner 3: FORTH Contribution

Fast Inversion Methods (WP3)Jorge Ripoll, Athanasios Zacharopoulos,

Giannis Zacharakis, Rosy FavicchioIESL – FORTH

Greece


Outline

Main Achievements in 2009/2010:

I. User Friendly Inversion Software (Deliverable 3.5)

II. Spectral Unmixing Algorithm (Deliverable 3.4)

III.Fast Inversion Method: Matrix Free Method (Deliverables 3.1 and 3.3) – Milestone 3.3


Collaborations

UCL

FORTH

CEA-LIME

HGGM

ETH

Matrix-Free Algorithm FMT test Data Generation

FMT-XCT data inplemetationBasic FMT principles

User Friendly software testing


I. User Friendly Software

• One-bottom Inversion software• Software for Fast raw-data analysis• Automatic report generation• Export to NIfTI format


REFLECTIONTRANSMISSION




Running the FMT experiment



RAW image analysis



12 3

4 5

6

7 8 9

10 11 12

13

ONE BOTTON INVERSION

Batch inverting data



Automated Report in Word Format


II. Spectral Unmixing Algorithm

M. Simantiraki, R. Favicchio, S. Psycharakis, G. Zacharakis and J. Ripoll, “Multispectral unmixing of fluorescence molecular tomography data”, J. of Inn. Opt. Health Sci. Vol. 2(4), 353–364 (2009).


II. Fast Inversion Algorithms

II. Fast Inversion AlgorithmsAthanasios Zacharopoulos & Simon Arridge

(UCL <> FORTH collaboration)


FUTURE WORK

FUTURE WORK:• Implementation of XCT data into user-friendly

software• Multi-Spectral Matrix-Free code• Matrix-Free & Data Compression Approach (UCL)• Implementation of Matrix-Free code in User-friendly

environment• User-Friendly Implementation of Priors from XCT

data for FMT-XCT data. • Test experimental ihmonogeneous FMT-XCT

phantoms


FMT-XCT

Fast Matrix Free MethodAthanasios Zacharopoulos

March 2010


• Improve resolution of FMT reconstructions

• Deal with large number of data• Reduce memory requirements• Reduce Computational Time• In-Vivo Reconstructions• Good Quantification properties• Realistic Geometries (XCT-MRI)


Forward Model

• Step1: Excitation Wavelength

Kx .φx = q • Step2: Fluorescence

Wavelength : Kf .φf = h.φx

• Forward ModelF(h) = A.h = M.[ Kf -1 .h .Kx-1.q]

• TOAST FEM code http://web4.cs.ucl.ac.uk/research/vis/toast/

φx

h

φf

Fluorochrome Concentration


Inverse Problem

• Find concentration for fluorochrome h’ so that:

h’= min ||gmeas-F (h’)||2

• Using a Gauss Newton scheme: (ATA+λI ).h’ = AT gmeas

• Where the Jacobian (weighting matrix) is given by:

A = φx x φf+

Kf φf+ = M Kx φx = q

n : number of nodes <10.000NoS : number of sources ~ 36NoD : number of detectors ~ 2000

NoS x NoD = 72000

n : number of nodes <10.000NoS : number of sources ~ 36NoD : number of detectors ~ 2000

NoS x NoD = 72000

An

NoS x N

oD


Matrix Free (ATA+λI ).h’ = AT gmeas

1. Remove Matrix Multiplications

ATA . h2. Replace Matrix times Vector

products with Vector times Vector products

3. Solve in respect to Sources rather than Detectors

AT

NoS x NoD

y

NoS x N

oD


Matrix FreeUse GMRES solver

iteratively


Matrix Free1. Multispectral Reconstructions


Matrix Free2. In-Vivo Reconstructions and

quantification



Quantification



quantification



Quantification

Method n. of measurements

Time Memory

Explicit Jacobian 56448 16 Min. 9.427 Sec 5.2 Gb

Matrix-Free 56448 0 Min. 16.95 sec 209 Mb


Matrix Free3. Realistic Geometries Prior

Information


Matrix Free3. Realistic Geometries Prior

Information 5% Gaussian Noise

Target Reconstruction


Future1. Reconstruction with XCT

geometry.2. Need Data!!3. Parametric Surfaces.4. Spherical Harmonics for

Prior information.

Thank you

J. Ripoll, Crete 2010 Partner 3: FORTH Contribution Fast Inversion Methods (WP3) Jorge Ripoll,...

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