j. ripoll, crete 2010 partner 3: forth contribution fast inversion methods (wp3) jorge ripoll,...
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J. Ripoll, Crete 2010
Partner 3: FORTH Contribution
Fast Inversion Methods (WP3)Jorge Ripoll, Athanasios Zacharopoulos,
Giannis Zacharakis, Rosy FavicchioIESL – FORTH
Greece
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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
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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
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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
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J. Ripoll, Crete 2010
REFLECTIONTRANSMISSION
I. User Friendly Software
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J. Ripoll, Crete 2010
I. User Friendly Software
Running the FMT experiment
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J. Ripoll, Crete 2010
I. User Friendly Software
RAW image analysis
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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
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J. Ripoll, Crete 2010
I. User Friendly Software
Automated Report in Word Format
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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).
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J. Ripoll, Crete 2010
II. Fast Inversion Algorithms
II. Fast Inversion AlgorithmsAthanasios Zacharopoulos & Simon Arridge
(UCL <> FORTH collaboration)
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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
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J. Ripoll, Crete 2010
FMT-XCT
Fast Matrix Free MethodAthanasios Zacharopoulos
March 2010
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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)
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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
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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
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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
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J. Ripoll, Crete 2010
Matrix FreeUse GMRES solver
iteratively
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J. Ripoll, Crete 2010
Matrix Free1. Multispectral Reconstructions
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J. Ripoll, Crete 2010
Matrix Free1. Multispectral Reconstructions
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J. Ripoll, Crete 2010
Matrix Free1. Multispectral Reconstructions
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J. Ripoll, Crete 2010
Matrix Free2. In-Vivo Reconstructions and
quantification
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J. Ripoll, Crete 2010
Matrix Free2. In-Vivo Reconstructions and
Quantification
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J. Ripoll, Crete 2010
Matrix Free2. In-Vivo Reconstructions and
quantification
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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
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J. Ripoll, Crete 2010
Matrix Free3. Realistic Geometries Prior
Information
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J. Ripoll, Crete 2010
Matrix Free3. Realistic Geometries Prior
Information 5% Gaussian Noise
Target Reconstruction
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J. Ripoll, Crete 2010
Future1. Reconstruction with XCT
geometry.2. Need Data!!3. Parametric Surfaces.4. Spherical Harmonics for
Prior information.
Thank you