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

J. Ripoll, Crete 2010

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

J. Ripoll, Crete 2010

Collaborations

UCL

FORTH

CEA-LIME

HGGM

ETH

Matrix-Free Algorithm FMT test Data Generation

FMT-XCT data inplemetationBasic FMT principles

User Friendly software testing

J. Ripoll, Crete 2010

I. User Friendly Software

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

J. Ripoll, Crete 2010

REFLECTIONTRANSMISSION

I. User Friendly Software

J. Ripoll, Crete 2010

I. User Friendly Software

Running the FMT experiment

J. Ripoll, Crete 2010

I. User Friendly Software

RAW image analysis

J. Ripoll, Crete 2010

I. User Friendly Software

12 3

4 5

6

7 8 9

10 11 12

13

ONE BOTTON INVERSION

Batch inverting data

J. Ripoll, Crete 2010

I. User Friendly Software

Automated Report in Word Format

J. Ripoll, Crete 2010

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).

J. Ripoll, Crete 2010

II. Fast Inversion Algorithms

II. Fast Inversion AlgorithmsAthanasios Zacharopoulos & Simon Arridge

(UCL <> FORTH collaboration)

J. Ripoll, Crete 2010

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

J. Ripoll, Crete 2010

FMT-XCT

Fast Matrix Free MethodAthanasios Zacharopoulos

March 2010

J. Ripoll, Crete 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)

J. Ripoll, Crete 2010

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

J. Ripoll, Crete 2010

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

J. Ripoll, Crete 2010

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

J. Ripoll, Crete 2010

Matrix FreeUse GMRES solver

iteratively

J. Ripoll, Crete 2010

Matrix Free1. Multispectral Reconstructions

J. Ripoll, Crete 2010

Matrix Free1. Multispectral Reconstructions

J. Ripoll, Crete 2010

Matrix Free1. Multispectral Reconstructions

J. Ripoll, Crete 2010

Matrix Free2. In-Vivo Reconstructions and

quantification

J. Ripoll, Crete 2010

Matrix Free2. In-Vivo Reconstructions and

Quantification

J. Ripoll, Crete 2010

Matrix Free2. In-Vivo Reconstructions and

quantification

J. Ripoll, Crete 2010

Matrix Free2. In-Vivo Reconstructions and

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

J. Ripoll, Crete 2010

Matrix Free3. Realistic Geometries Prior

Information

J. Ripoll, Crete 2010

Matrix Free3. Realistic Geometries Prior

Information 5% Gaussian Noise

Target Reconstruction

J. Ripoll, Crete 2010

Future1. Reconstruction with XCT

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

Prior information.

Thank you