Compressive diffuse optical tomography: Noniterative exact reconstruction using joint sparsity

IEEE Transactions on Medical Imaging

Volumn 30, Issue 5, 2011, Pages 1129-1142

  Lee, Okkyun ^a   Kim, Jong Min ^a   Bresler, Yoram ^b   Ye, Jong Chul ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Diffuse optical tomography (DOT); generalized MUSIC criterion; joint sparsity; multiple measurement vector (MMV); p thresholding; simultaneous orthogonal matching pursuit (S OMP)

Indexed keywords

DIFFUSE OPTICAL TOMOGRAPHY; GENERALIZED MUSIC CRITERION; JOINT SPARSITY; MULTIPLE MEASUREMENT VECTOR (MMV); ORTHOGONAL MATCHING PURSUIT; THRESHOLDING;

ALGORITHMS; MEDICAL IMAGING; OPTICAL TOMOGRAPHY; SIGNAL PROCESSING; SIGNAL RECONSTRUCTION;

OPTICAL PROPERTIES;

ALGORITHM; ANIMAL; ARTICLE; COMPUTER SIMULATION; IMAGE PROCESSING; IMAGE QUALITY; INSTRUMENTATION; METHODOLOGY; MOUSE; OPTICAL TOMOGRAPHY; SIGNAL PROCESSING; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; IMAGE PROCESSING, COMPUTER-ASSISTED; MICE; MODELS, THEORETICAL; PHANTOMS, IMAGING; SIGNAL PROCESSING, COMPUTER-ASSISTED; TOMOGRAPHY, OPTICAL;

EID: 79955634911     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2011.2125983     Document Type: Article

References (63)

1. C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, and B. Dennery, "Visualizing gene expression in living mammals using a biolumines-cent reporter," Photochem. Photobiol., no. 66, pp. 523-531, 1997. (Pubitemid 127470201)
2. C. L. Hutchinson, T. L. Troy, and E. M. Sevick-Muraca, "Fluorescence lifetime determination in tissues and other random media from measurement of excitation and emission kinetics," Appl. Opt., no. 35, pp. 2325-2332, 1996. (Pubitemid 126629542)
3. B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol., vol. 40, pp. 1709-1729, 1995.
4. R. Weissleder, "Scaling down imaging: Molecular mapping of cancer in mice," Nature Rev. Cancer, vol. 2, pp. 1-8, 2002.
5. R. Weissleder and V. Ntziachristos, "Shedding light onto live molecular targets," Nature Med., vol. 9, no. 1, pp. 123-128, 2003. (Pubitemid 36098273)
6. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, "Optical image reconstruction using frequency-domain data: Simulation and experiment," J. Opt. Soc. Am. A, vol. 13, no. 2, pp. 253-266, Feb. 1996. (Pubitemid 126548522)
7. Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, "Frequency domain optical imaging of absorption and scattering distributions by a Born iterative method," J. Opt. Soc. Am. A, vol. 14, no. 1, pp. 325-342, Jan. 1997. (Pubitemid 127573831)
8. V. A. Markel, J. A. O'Sullivan, and J. C. Schotland, "Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas," J. Opt. Soc. Am. A, vol. 20, no. 5, pp. 903-912, May 2003.
9. J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, "Optical diffusion tomography using iterative coordinate descent optimization in a Bayesian framework," J. Opt. Soc. Am. A, vol. 16, no. 10, pp. 2400-2412, Oct. 1999. (Pubitemid 129652130)
10. J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, "Nonlinear multigrid algorithms for Bayesian optical diffusion tomography," IEEE Trans. Image Process., vol. 10, no. 6, pp. 909-922, Jun. 2001. (Pubitemid 32498465)
11. V. Ntziachristos and R. Weissleder, "Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation," Opt. Lett., vol. 26, no. 12, pp. 893-895, Jun. 2001. (Pubitemid 33693607)
12. V. A. Markel and J. C. Schotland, "Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas," J. Opt. Soc. Am. A, vol. 18, no. 6, pp. 1336-1347, Jun. 2001.
13. V. A. Markel and J. C. Schotland, "Inverse problem in optical diffusion tomography. II. Role of boundary conditions," J. Opt. Soc. Am. A, vol. 19, no. 3, pp. 558-566, 2002.
14. V. A. Markel, V. Mital, and J. C. Schotland, "Inverse problem in optical diffusion tomography. III. inversion formulas and singular-value decomposition," J. Opt. Soc. Am. A, vol. 20, no. 5, pp. 890-902, May 2003.
15. J. Chen and X. Huo, "Theoretical results on sparse representations of multiple measurement vectors," IEEE Trans. Signal Process., vol. 54, no. 12, pp. 4634-4643, Dec. 2006. (Pubitemid 46405606)
16. J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process., vol. 86, no. 3, pp. 572-588, 2006. (Pubitemid 43106572)
17. R. Gribonval, H. Rauhut, K. Schnass, and P. Vandergheynst, "Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms," J. Fourier Anal. Appl., vol. 14, no. 5, pp. 655-687, 2008.
18. J. M. Kim, O. K. Lee, and J. C. Ye, "Compressive MUSIC: A missing link between compressive sensing and array signal processing," 2010.
19. K. Lee and Y. Bresler, "Subspace-Augmented MUSIC for Joint Sparse Recovery," .
20. M. F. Duarte, S. Sarvotham, D. Baron, M. B. Wakin, and R. G. Bara-niuk, "Distributed compressed sensing of jointly sparse signals," in Asilomar Conf. Signals, Sys. Comput., 2005, pp. 1537-1541. (Pubitemid 46350567)
21. J. C. Ye, S. Y. Lee, and Y. Bresler, "Exact reconstruction formula for diffuse optical tomography using simultaneous sparse representation," in Proc. 2008 IEEE Int. Symp. Biomed. Imag.: From Nano to Macro, Paris, France, May 2008, pp. 1621-1624.
22. L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations. New York: Wiley, 2000.
23. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering. Cambridge, U.K.: Cambridge Univ. Press, 2006.
24. A. C. Fannjiang, "Compressive inverse scattering: I. High-frequency SIMO/MISO and MIMO measurements," Inverse Problems, vol. 26, pp. 1-29, 2010.
25. A. Kirsch, "Characterization of the shape of a scattering obstacle using the spectral data of the far field operator," Inverse Problems, vol. 14, pp. 1489-1512, 1998. (Pubitemid 128553316)
26. M. Cheney, "The linear sampling method and the MUSIC algorithm," Inverse Problems, vol. 17, no. 4, pp. 591-596, 2001.
27. E. A. Marengo and F. K. Gruber, "Subspace-based localization and inverse scattering of multiply scattering point targets," EURASIP J. Adv. Signal Process., vol. 17342, p. 16, 2007.
28. M. Pfister and B. Scholz, "Localization of fluorescence spots with space-space MUSIC for mammographylike measurement systems," J. Biomed. Opt., vol. 9, p. 481, 2004.
29. A. C. Fannjiang, "The MUSIC algorithm for sparse objects: A compressed sensing analysis," Inverse Problems, vol. 27, p. 035013, 2011.
30. D. P. Wipf, "Bayesian methods for finding sparse representations," Ph.D. dissertation, Univ. California, San Diego, 2006.
31. J. A. Tropp, "Algorithms for simultaneous sparse approximation. Part II: Convex relaxation," Signal Process., vol. 86, no. 3, pp. 589-602, 2006. (Pubitemid 43106573)
32. M. Mishali and Y. C. Eldar, "Reduce and boost: Recovering arbitrary sets of jointly sparse vectors," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4692-4702, Oct. 2010.
33. Y. C. Eldar, P. Kuppinger, and H. Bolcskei, "Block-sparse signals: Uncertainty relations and efficient recovery," IEEE Trans. Signal Process., vol. 58, pp. 3042-3054, 2010.
34. D. L. Donoho, Neighborly polytopes and sparse solution of under-determined linear equations Dept. Stat., Stanford Univ., Tech. Rep., 2005.
35. D. L. Donoho and M. Elad, "Optimally sparse representation in general (non-orthogonal) dictionaries via Zj minimization," Proc. Nat. Acad. Sci. USA, vol. 100, no. 5, pp. 2197-2202, 2003. (Pubitemid 36297476)
36. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
37. A. Aldroubi, "Oblique projections in atomic spaces," Proc. Amer. Math. Soc, vol. 124, pp. 2051-2060, 1996.
38. M. Unser and A. Aldroubi, "A general sampling theory for non-ideal acquisition devices," IEEE Trans. Signal Process., vol. 42, pp. 2915-2925, 1994.
39. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory," Appl. Opt., vol. 36, pp. 4587-4599, 1997. (Pubitemid 127642811)
40. V. Ntziachristos and B. Chance, "Probing physiology and molecular function using optical imaging: Applications to breast cancer," Breast Cancer Res., vol. 3, pp. 41-46, 2001. (Pubitemid 32223652)
41. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag., vol. 18, no. 6, pp. 57-75, Nov. 2001. (Pubitemid 33090780)
42. M. Pfister and B. Scholz, "Localization of fluorescence spots with space-space music for mammographylike measurement systems," J. Biomed. Opt., vol. 9, pp. 481-487, May/Jun. 2004.
43. S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, "Imaging complex structures with diffuse light," Opt. Express, vol. 16, no. 7, pp. 5048-5060, 2008. (Pubitemid 351483468)
44. V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence-mediated tomography resolves protease activity in vivo," Nat. Med, vol. 8, pp. 757-760, 2002. (Pubitemid 34778731)
45. M. A. Franceschini and D. A. Boas, "Noninvasive measurement of neuronal activity with near-infrared optical imaging," NeuroImage, vol. 21, no. 1, pp. 372-386, 2004. (Pubitemid 38115028)
46. P. Feng, "Universal minimum-rate sampling and spectrum-blind reconstruction for multiband signals," Ph.D. dissertation, Univ. Illinois, Ur-bana-Champaign, 1997.
47. M. E. Davies and Y. C. Eldar, "Rank awareness in joint sparse recovery," 2010.
48. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
49. R. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276-280, Mar. 1986. (Pubitemid 16613653)
50. P. Feng and Y. Bresler, "Spectrum-blind minimum-rate sampling and reconstruction of multiband signals," in Proc. ICASSP, Atlanta, GA, May 1996, vol. 3, pp. 1688-1691.
51. Y. C. Eldar and H. Rauhut, "Average case anlysis of multichannel sparse recovery using convex relaxation," IEEE Trans. Information Theory, vol. 56, pp. 505-519, 2010.
52. V. Ntziachristos, C. Bremer, and R. Weissleder, "Fluorescence imaging with near-infrared light: New technological advances that enable in vivo molecular imaging," Eur. Radiol., vol. 13, no. 1, pp. 195-208, Jan. 2003. (Pubitemid 36790510)
53. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, "Non-contact fluorescence optical tomography with scanning patterned illumination," Opt. Express, vol. 19, no. 14, pp. 6516-6534, Jul. 2006. (Pubitemid 44036385)
54. T. Lasser and V. Ntziachristos, "Optimization of 360 ° projection fluorescence molecular tomography," Med. Image Anal., vol. 11, pp. 389-399, Apr. 2007. (Pubitemid 46979978)
55. J. P. Culver, V. Ntziachristos, M. J. Holbrooke, and A. G. Yodh, "Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis," Opt. Lett., vol. 26, no. 10, pp. 701-703, May 15, 2001. (Pubitemid 33693268)
56. J. Dutta, S. Ahn, A. A. Joshi, and R. M. Leahy, "Illumination pattern optimization for fluorescence tomography: Theory and simulation studies," Phys. Med. Biol, vol. 55, no. 10, pp. 2961-2982, Apr. 2010.
57. M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorbing imaging: I," Inverse Problems, vol. 23, pp. 1115-1133, 2007. (Pubitemid 46838845)
58. K. Schnass and P. Vandergheynst, "Dictionary preconditioning for greedy algorithms," IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1994-2002, May 2008.
59. B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, "Digi-mouse: A 3-D whole body mouse atlas from CT and cryosection data," Phys. Med. Biol, vol. 52, pp. 577-587, 2007. (Pubitemid 46646432)
60. Q. Fang and D. A. Boas, "Monte Carlo simulation of photon migration in 3-D turbid media accelerated by graphics processing units," Opt. Express, vol. 17, no. 22, pp. 20178-20190, Oct. 2009.
61. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: A computer simulation feasibility study," Phys. Med. Biol, vol. 50, pp. 4225-4241, 2005. (Pubitemid 41225267)
62. S. A. Prahl, Optical properties spectra 2001, Oregon Medical Laser Clinic [Online]. Available: http://omlc.ogi.edu/spectra/index.html
63. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, "Comparing images using the Hausdorff distance," IEEE Trans. Pattern Anal. Mach. Intell, vol. 15, no. 9, pp. 850-863, Sep. 1993.