Fluorescence diffuse optical tomography using the split Bregman method

Medical Physics

Volumn 38, Issue 11, 2011, Pages 6275-6284

  Abascal, J F P J ^a   Chamorro Servent, J ^a   Aguirre, J ^a   Arridge, S ^b   Correia, T ^b   Ripoll, J ^c   Vaquero, J J ^a   Desco, M ^d  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c INSTITUTE OF COMPUTER SCIENCE   (Greece)

^d HOSPITAL GENERAL UNIVERSITARIO GREGORIO MARAÑÓN   (Spain)

Author keywords

constrained optimization; diffuse optical tomography; L1 regularization; split Bregman; total variation

Indexed keywords

CONSTRAINED OPTIMIZATION; FLUORESCENCE; IMAGE ENHANCEMENT; ITERATIVE METHODS; OPTICAL TOMOGRAPHY; SIGNAL TO NOISE RATIO;

BREGMAN; DIFFUSE OPTICAL TOMOGRAPHY; FLUORESCENCE DIFFUSE OPTICAL TOMOGRAPHY; L1 REGULARIZATIONS; NON-NEGATIVITY CONSTRAINTS; RECONSTRUCTION PROBLEMS; TOTAL VARIATION; UNCONSTRAINED OPTIMIZATION;

IMAGE RECONSTRUCTION;

EID: 80855134310     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.3656063     Document Type: Article

References (41)

1. E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, A submillimeter resolution fluorescence molecular imaging system for small animal imaging., Med. Phys. 30, 901-911 (2003). 10.1118/1.1568977 (Pubitemid 36578694)
2. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, Looking and listening to light: the evolution of whole-body photonic imaging., Nat. Biotechnol. 23, 313-320 (2005). 10.1038/nbt1074 (Pubitemid 41094419)
3. S. Patwardhan, S. Bloch, S. Achilefu, and J. Culver, Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice., Opt. Express 13, 2564-2577 (2005). 10.1364/OPEX.13.002564 (Pubitemid 40899217)
4. T. Lasser and V. Ntziachristos, Optimization of 360 degrees projection fluorescence molecular tomography., Med. Image Anal. 11, 389-399 (2007). 10.1016/j.media.2007.04.003 (Pubitemid 46979978)
5. A. Martin, J. Aguirre, A. Sarasa, D. Tsoukatou, A. Garofalakis, H. Meyer, C. Mamalaki, J. Ripoll, and A. M. Planas, Imaging changes in lymphoid organs in vivo after brain ischemia with three-dimensional fluorescence molecular tomography in transgenic mice expressing green fluorescent protein in T lymphocytes., Mol. Imaging 7, 157-167 (2008). 10.2310/7290.2008.00016
6. S. R. Arridge, M. Hiraoka, and D. T. Delpy, A finite element approach for modelling photon transport in tissue., Med. Phys. 20, 299-309 (1993). 10.1118/1.597069 (Pubitemid 23136192)
7. X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, and B. Chance, Projection access order in algebraic reconstruction technique for diffuse optical tomography., Phys. Med. Biol. 47, N1-N10 (2002). 10.1088/0031-9155/47/1/ 401 (Pubitemid 34071356)
8. A. Soubret, J. Ripoll, and V. Ntziachristos, Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio., IEEE Trans. Med. Imaging 24, 1377-1386 (2005). 10.1109/TMI.2005.857213 (Pubitemid 41463574)
9. A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, Three-dimensional in vivo fluorescence diffusive optical tomography of breast cancer in humans., Opt. Express 15, 6696-6716 (2007). 10.1364/OE.15.006696 (Pubitemid 46827669)
10. D. Hyde, R. Schulz, D. Brooks, E. Miller, and V. Ntziachristos, Performance dependence of hybrid x-ray computed tomography/fluorescence molecular tomography on the optical forward problem., J. Opt. Soc. Am. A 26, 919-923 (2009). 10.1364/JOSAA.26.000919
11. L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms., Physica D 60, 259-268 (1992). 10.1016/0167-2789(92) 90242-F
12. C. R. Vogel, Computational Methods for Inverse Problems (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002).
13. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).
14. S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, An iterative regularization method for total variation-based image restoration., Multiscale Model. Simul. 4, 460-489 (2005). 10.1137/040605412 (Pubitemid 43885248)
15. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, Bregman iterative algorithms for l1-minimization with applications to compressed sensing., SIAM J. Imaging Sci. 1, 143-168 (2008). 10.1137/070703983
16. T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems., SIAM J. Imaging Sci. 2, 323-343 (2009). 10.1137/080725891
17. E. Esser, Applications of Lagrangian-based alternating direction methods and connections to split Bregman., UCLA CAM Technical Report, 9-31 (2009).
18. M. Lustig, D. Donoho, and J. M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging., Magn. Reson. Med. 58, 1182-1195 (2007). 10.1002/mrm.v58:6 (Pubitemid 350234205)
19. K. D. Paulsen and H. Jiang, Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization., Appl. Opt. 35, 3447-58 (1996). 10.1364/AO.35.003447 (Pubitemid 126622158)
20. A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information., Meas. Sci. Technol. 18, 87-95 (2007). 10.1088/0957-0233/18/1/011 (Pubitemid 46485525)
21. H. Gao and H. Zhao, Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization., Opt. Express 18, 1854-1871 (2010). 10.1364/OE.18.001854
22. H. Gao and H. Zhao, Multilevel bioluminescence tomography based on radiative transfer equation Part 2: Total variation and l1 data fidelity., Opt. Express 18, 2894-2912 (2010). 10.1364/OE.18.002894
23. D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization., Opt. Express 18, 8630-8648 (2010). 10.1364/OE.18.008630
24. M. Freiberger, C. Clason, and H. Scharfetter, Total variation regularization for nonlinear fluorescence tomography with an augmented lagrangian splitting approach., Appl. Opt. 49, 3741-3747 (2010). 10.1364/AO.49.003741
25. T. Correia, J. Aguirre, A. Sisniega, J. Chamorro-Servent, J. Abascal, J. J. Vaquero, M. Desco, V. Kolehmainen, and S. Arridge, Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information., Biomed. Opt. Express 2, 2632-2648 (2011). 10.1364/BOE.2.002632
26. S. Setzer, G. Steidl, and T. Teuber, Deblurring Poissonian images by split Bregman techniques., J. Visual Commun. Image Representation 21, 193-199 (2010). 10.1016/j.jvcir.2009.10.006
27. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, Fluorescence optical diffusion tomography., Appl. Opt. 42, 3081-3094 (2003). 10.1364/AO.42.003081
28. V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, Diffuse optical tomography of highly heterogeneous media., IEEE Trans. Medical Imaging 20, 470-478 (2001). 10.1109/42.929613 (Pubitemid 32657851)
29. V. Ntziachristos and R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation., Opt. Lett. 26, 893-895 (2001). 10.1364/OL.26.000893 (Pubitemid 33693607)
30. R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, Hybrid system for simultaneous fluorescence and x-ray computed tomography., IEEE Trans. Med. Imaging 29, 465-473 (2010). 10.1109/TMI.2009.2035310
31. M. Schweiger, Application of the finite element method in infrared image reconstruction of scattering media., Ph.D. thesis, University College London, London, UK, 1994.
32. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, The finite element method for the propagation of light in scattering media: Boundary and source conditions., Med. Phys. 22, 1779-1792 (1995). 10.1118/1.597634
33. M. Schweiger, S. R. Arridge, and I. Nissila, Gauss-Newton method for image reconstruction in diffuse optical tomography., Phys. Med. Biol. 50, 2365-2386 (2005). 10.1088/0031-9155/50/10/013 (Pubitemid 40767821)
34. A. Banerjee, S. Merugu, and I. S. Dhillon, Clustering with Bregman divergences., J. Mach. Learn. Res. 6, 1705-1749 (2005).
35. J. Ripoll, R. B. Schulz, and V. Ntziachristos, Free-space propagation of diffuse light: Theory and experiments., Phys. Rev. Lett. 18, 103901 (2003). 10.1103/PhysRevLett.91.103901
36. J. Ripoll and V. Ntziachristos, Imaging scattering media from a distance: theory and applications of noncontact optical tomography., Mod. Phys. Lett. B 18, 1403-1431 (2004). 10.1142/S0217984904007864 (Pubitemid 41103461)
37. D. Boas, Diffuse Photon Probes of Structural and Dynamical Properties of Turbid Media: Theory and Biomedical Applications., Ph.D. thesis, University of Pennsylvania, Philadelphia, 1996.
38. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, A solid tissue phantom for photon migration studies., Phys. Med. Biol. 42, 1971-1979 (1997). 10.1088/0031-9155/42/10/011 (Pubitemid 27448998)
39. L. He, T.-C. Chang, S. Osher, T. Fang, and P. Speier, MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods., UCLA CAM Technical Report, 6-35 (2006).
40. H. Gao, Y. Lin, G. Gulsen, and H. Zhao, Fully linear reconstruction method for fluorescence yield and lifetime through inverse complex-source formulation., Opt. Express 35, 1899-1901 (2010). 10.1364/OL.35.001899
41. H. Gao, S. Osher, and H. Zhao, Quantitative photoacoustic tomography., UCLA CAM Report, 11-28. (Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographies. Lecture Notes in Mathematics), Springer-Verlag, Berlin Heidelberg, 2035, 131-158 (2012).