1. J. Ripoll, Crete 2010 Partner 3: FORTH Contribution Fast Inversion Methods (WP3) Jorge Ripoll, Athanasios Zacharopoulos, Giannis Zacharakis, Rosy Favicchio IESL – FORTH Greece

2. 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

3. J. Ripoll, Crete 2010 Collaborations UCL FORTH CEA-LIME HGGM ETH Matrix-Free Algorithm FMT test Data Generation FMT-XCT data inplemetation Basic FMT principles User Friendly software testing

4. 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

5. J. Ripoll, Crete 2010 REFLECTION TRANSMISSION I. User Friendly Software

6. J. Ripoll, Crete 2010 I. User Friendly Software Running the FMT experiment

7. J. Ripoll, Crete 2010 I. User Friendly Software RAW image analysis

8. J. Ripoll, Crete 2010 I. User Friendly Software ONE BOTTON INVERSION Batch inverting data

9. J. Ripoll, Crete 2010 I. User Friendly Software Automated Report in Word Format

10. 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).

11. J. Ripoll, Crete 2010 II. Fast Inversion Algorithms Athanasios Zacharopoulos & Simon Arridge (UCL <> FORTH collaboration)

12. 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

13. J. Ripoll, Crete 2010 FMT-XCT Fast Matrix Free Method Athanasios Zacharopoulos March 2010

14. 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)

15. J. Ripoll, Crete 2010 Forward Model Step1: Excitation Wavelength K x. φ x = q Step2: Fluorescence Wavelength : K f. φ f = h. φ x Forward Model F(h) = A.h = M.[ K f -1. h.K x-1. q] TOAST FEM code http://web4.cs.ucl.ac.uk/research/vis/toast/ φxφx h φfφf Fluorochrome Concentration

16. J. Ripoll, Crete 2010 Inverse Problem Find concentration for fluorochrome h’ so that: h’= min ||g meas -F (h’)|| 2 Using a Gauss Newton scheme: (A T A+ λ I ).h’ = A T g meas Where the Jacobian (weighting matrix) is given by: A = φ x x φ f+ K f φ f+ = M K x φ x = q n : number of nodes <10.000 NoS : number of sources ~ 36 NoD : number of detectors ~ 2000 NoS x NoD = 72000 n : number of nodes <10.000 NoS : number of sources ~ 36 NoD : number of detectors ~ 2000 NoS x NoD = 72000 A n NoS x NoD

17. J. Ripoll, Crete 2010 Matrix Free (A T A+ λ I ).h’ = A T g meas 1.Remove Matrix Multiplications A T A. h 2.Replace Matrix times Vector products with Vector times Vector products 3.Solve in respect to Sources rather than Detectors ATAT NoS x NoD y

18. J. Ripoll, Crete 2010 Matrix Free Use GMRES solver iteratively

19. J. Ripoll, Crete 2010 Matrix Free 1.Multispectral Reconstructions

20. J. Ripoll, Crete 2010 Matrix Free 1.Multispectral Reconstructions

21. J. Ripoll, Crete 2010 Matrix Free 1.Multispectral Reconstructions

22. J. Ripoll, Crete 2010 Matrix Free 2. In-Vivo Reconstructions and quantification

23. J. Ripoll, Crete 2010 Matrix Free 2. In-Vivo Reconstructions and Quantification

24. J. Ripoll, Crete 2010 Matrix Free 2. In-Vivo Reconstructions and quantification

25. J. Ripoll, Crete 2010 Matrix Free 2. In-Vivo Reconstructions and Quantification Methodn. of measurements TimeMemory Explicit Jacobian56448 16 Min. 9.427 Sec5.2 Gb Matrix-Free 56448 0 Min. 16.95 sec209 Mb

26. J. Ripoll, Crete 2010 Matrix Free 3. Realistic Geometries Prior Information

27. J. Ripoll, Crete 2010 Matrix Free 3. Realistic Geometries Prior Information 5% Gaussian Noise TargetReconstruction

28. J. Ripoll, Crete 2010 Future 1.Reconstruction with XCT geometry. 2.Need Data!! 3.Parametric Surfaces. 4.Spherical Harmonics for Prior information. Thank you