Noniterative MAP reconstruction using sparse matrix representations

IEEE Transactions on Image Processing

Volumn 18, Issue 9, 2009, Pages 2085-2099

  Cao, Guangzhi ^a   Bouman, Charles A ^a   Webb, Kevin J ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Inverse problems; Matrix source coding; Noniterative reconstruction; Optical tomography; Sparse matrix representation

Indexed keywords

DISTORTION METRICS; INVERSE MATRIX; INVERSE TRANSFORMS; ITERATIVE RECONSTRUCTION; LOSSY SOURCE CODING; MAP ALGORITHMS; MAP RECONSTRUCTION; MATRIX; MATRIX SOURCE CODING; MATRIX TRANSFORMATION; MATRIX TRANSFORMS; MATRIX-VECTOR PRODUCTS; MAXIMUM A POSTERIORI; MEASUREMENT DATA; NON-ITERATIVE; NONITERATIVE RECONSTRUCTION; OFF-LINE COMPUTATION; ORDERS OF MAGNITUDE; ORTHONORMAL; ORTHONORMAL TRANSFORM; PRECOMPUTE; SOURCE-CODING; SPARSE MATRICES; SPARSE MATRIX REPRESENTATION; TOMOGRAPHIC RECONSTRUCTION;

COMMUNICATION CHANNELS (INFORMATION THEORY); DIFFERENTIAL EQUATIONS; FAST FOURIER TRANSFORMS; INVERSE PROBLEMS; LIGHT TRANSMISSION; MATHEMATICAL TRANSFORMATIONS; ONLINE SEARCHING; OPTICAL TOMOGRAPHY; REPAIR;

MATRIX ALGEBRA;

ALGORITHM; ARTICLE; FEMALE; FOURIER ANALYSIS; HUMAN; IMAGE PROCESSING; METHODOLOGY; NORMAL DISTRIBUTION; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY;

ALGORITHMS; FEMALE; FOURIER ANALYSIS; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MARKOV CHAINS; NORMAL DISTRIBUTION; PRINCIPAL COMPONENT ANALYSIS;

EID: 69349088165     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2023724     Document Type: Article

References (51)

1. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression Norwell, MA: Kluwer, 1991.
2. S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674-693, Jul. 1989.
3. E. E. Fenimore and T. M. Cannon, "Coded aperture imaging with uniformly redundant arrays," Appl. Opt., vol. 17, no. 3, p. 337, 1978.
4. Y. Bresler, M. Gastpar, and R. Venkataramani, "Image compression on-the-fly by universal sampling in fourier imaging systems," presented at the IEEE Information Theory Workop on Detection, Estimation, Classification, and Imaging, Feb. 1999.
5. E. J. Candes, "Compressive sampling," presented at the Int. Congr. Mathematicians, Madrid, Spain, Aug. 2006.
6. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
7. C. F. Van Loan, Computational Frameworks for the Fast Fourier Transform. Philadelphia, PA: SIAM, 1992.
8. P. A. Regalia and S. K. Mitra, "Kronecker products, unitary matrices and signal processing applications," SIAM Rev., vol. 31, no. 4, pp. 586-613, Dec. 1989.
9. S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.
10. T. Hebert and R. Leahy, "A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors," IEEE Trans. Med. Imag., vol. 8, no. 2, pp. 194-202, Jun. 1989.
11. K. Sauer and C. A. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 534-548, Feb. 1993.
12. J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, "A three-dimensional statistical approach to improved image quality for multislice helical CT," Med. Phys., vol. 34, no. 11, pp. 4526-4544, 2007.
13. S. Geman and D. E. McClure, "Statistical methods for tomographic image reconstruction," Bull. Int. Statist. Inst., pp. LII-4:5-21, 1987.
14. E. Levitan and G. T. Herman, "A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography," IEEE Trans. Med. Imag., vol. 6, no. 3, pp. 185-192, Mar. 1987.
15. P. J. Green, "Bayesian reconstructions from emission tomography data using a modified EM algorithm," IEEE Trans. Med. Imag., vol. 9, no. 1, pp. 84-93, Jan. 1990.
16. G. Cao, C. A. Bouman, and K. J. Webb, "Fast and efficient stored matrix techniques for optical tomography," in Proc. 40th Asilomar Conf. Signals, Systems, and Computers, Oct. 2006.
17. G. Cao, C. A. Bouman, and K. J. Webb, "Fast reconstruction algorithms for optical tomography using sparse matrix representations," presented at the IEEE Int. Symp. Biomedical Imaging, Apr. 2007.
18. W. Givens, "Computation of plane unitary rotations transforming a general matrix to triangular form," J. SIAM, vol. 6, no. 1, pp. 26-50, Mar. 1958.
19. H. Rutishauser, "The jacobi method for real symmetric matrices," Numer. Math., vol. 9, pp. 1-10, 1966.
20. P. A. Regalia, "An adaptive unit norm filter with applications to signal analysis and Karhunen-Loeve transformations," IEEE Trans. Circuits Syst., vol. 37, no. 5, pp. 646-649, May 1990.
21. P. Comon, "Independent component analysis: A new concept?," Signal Process., vol. 36, no. 3, pp. 287-314, 1994.
22. N. Delfosse and P. Loubaton, "Adaptive blind separation of independent sources: A deflation approach," Signal Process., vol. 45, no. 1, pp. 59-83, 1995.
23. E. Moreau and J.-C. Pesquet, "Generalized contrasts for multichannel blind deconvolution of linear systems," IEEE Signal Process. Lett. vol. 4, no. 6, pp. 182-183, Jun. 1997.
24. A. Hyvarinen and E. Oja, "Independent component analysis: Algorithms and applications," Neural Netw., vol. 13, pp. 411-430, May-Jun. 2000.
25. A. Soman and P. Vaidyanathan, "Paraunitary filter banks and wavelet packets," in Proc. IEEE ICASSP, Mar. 1992, vol. 4, pp. 397-400.
26. A. B. Lee, B. Nadler, and L. Wasserman, "Treelets-an adaptive multiscale basis for sparse unordered data," Ann. Appl. Statist., vol. 2, no. 2, pp. 435-471, 2008.
27. G. Cao and C. Bouman, "Covariance estimation for high dimensional data vectors using the sparse matrix transform," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 2008, pp. 225-232.
28. A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol., vol. 50, pp. R1-R43, Feb. 2005.
29. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems. New York: Winston & Sons, 1977.
30. A. N. Netravali and B. G. Haskell, Digital Pictures: Representation, Compression, and Standards. New York: Plenum, 1995.
31. G. Golub and C. V. Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
32. D. Tretter and C. A. Bouman, "Optimal transforms for multispectral and multilayer image coding," IEEE Trans. Image Process., vol. 4, no. 3, pp. 296-308, Mar. 1995.
33. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, "Image coding using wavelet transform," IEEE Trans. Image Process., vol. 1, no. 2, pp. 205-220, Apr. 1992.
34. P. Dragotti, G. Poggi, and A. Ragozini, "Compression of multispectral images by three-dimensional SPIHT algorithm," IEEE Trans. Geosci. Remote Sens., vol. 38, no. 1, pp. 416-428, Jan. 2000.
35. A. Said and W. A. Pearlman, "A new, fast, and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 3, pp. 243-250, Jun. 1996.
36. J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput., vol. 19, no. 90, pp. 297-301, Apr. 1965.
37. D. K. Hoffman, R. C. Raffenetti, and K. Ruedenberg, "Generalization of euler angles to n-dimensional orthogonal matrices," J. Math. Phys. vol. 13, no. 4, pp. 528-533, 1972.
38. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
39. J.-F. Cardoso, "High-order contrasts for independent component analysis," Neural Comput., vol. 11, no. 1, pp. 157-192, 1999.
40. J. Eriksson and V. Koivunen, "Characteristic-function-based independent component analysis," Signal Process., vol. 83, no. 10, pp. 2195-2208, 2003.
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.
42. 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., vol. 42, no. 16, pp. 3081-3094, Jun. 2003.
43. M. S. Patterson, J. D. Moultan, B. C. Wilson, K. W. Berndtand, and J. R. Lakowicz, "Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue," Appl. Opt., vol. 30, pp. 4474-4476, 1991.
44. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Refraction of diffuse photon density waves," Phys. Rev. Lett., vol. 69, pp. 2658-2661, 1992.
45. Q. Zhang, T. J. Brukilacchio, A. Li, J. J. S. T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, "Coregistered tomographic x-ray and optical breast imaging: Initial results," J. Biomed. Opt., vol. 10, no. 2, pp. 024033,1-9, Mar./Apr. 2005.
46. L. C. Enfield, A. P. Gibson, N. L. Everdell, D. T. Delpy, M. Schweiger, S. R. Arridge, C. Richardson, M. Keshtgar, M. Douek, and J. C. Hebden, "Three-dimensional time-resolved optical mammography of the uncompressed breast," Appl. Opt., vol. 46, no. 17, pp. 3628-3638, 2007.
47. 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. Amer. A, vol. 16, no. 10, pp. 2400-2412, Oct. 1999.
48. C. A. Bouman and K. Sauer, "A generalized Gaussian image model for edge-preserving MAP estimation," IEEE Trans. Image Process., vol. 2, no. 3, pp. 296-310, Jul. 1993.
49. I. Daubechies and W. Sweldens, "Factoring wavelet transforms into lifting steps," J. Fourier Anal. Appl., vol. 4, no. 3, pp. 247-269, May 1998.
50. R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, "Tomographic fluorescence imaging in tissue phantoms: A novel reconstruction algorithm and imaging geometry," IEEE Trans. Med. Imag., vol. 24, no. 2, pp. 137-154, Feb. 2005.
51. J. Wei, G. Cao, C. Bouman, and J. Allebach, "Fast space-varying convolution and its application in stray light reduction," presented at the SPIE/IS&T Conf. Computational Imaging VII, Jan. 2009.