A wide-angle view at iterated shrinkage algorithms

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6701, Issue , 2007, Pages

  Elad, M ^a   Matalon, B ^a   Shtok, J ^a   Zibulevsky, M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

1 norm; 2 norm; Dictionary; Iterated shrinkage; Optimization; Redundant; Sparse

Indexed keywords

ALGORITHMS; OPTICAL DATA PROCESSING; OPTICAL SIGNAL PROCESSING; OPTIMIZATION;

COMPARATIVE PERFORMANCE; SHRINKAGE ALGORITHMS;

ITERATIVE METHODS;

EID: 42149167847     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.741299     Document Type: Conference Paper

References (53)

1. T. Adeyemi and M.E. Davies, Sparse representations of images using overcomplete complex wavelets, IEEE SP 13th Workshop on Statistical Signal Processing, pages 805-809, Bordeaux, France, 17-20 July 2006.
2. J. Bioucas-Dias, Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors, IEEE Trans. on Image processing, 15(4):937-951, April 2006.
3. T. Blumensath and M.E. Davies, Iterative thresholding for sparse approximations, submitted to Journal of Fourier Analysis and Applications.
4. E.J. Candes, J. Romberg, and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. on Information Theory, 52(2):489-509, 2006.
5. S. Chen, S.A. Billings, and W. Luo, Orthogonal least squares methods and their application to non-linear system identification, International Journal of Control, 50(5): 1873-96, 1989.
6. S.S. Chen, D.L. Donoho, and M.A. Saunders, Atomic decomposition by basis pursuit, SIAM Journal on Scientific Computing, 20(1):33-61 (1998).
7. I. Daubechies, M. Fornasier, and I. Loris, Accelerated projected gradient method for linear inverse problems with sparsity Constraints, arXiv: 0706.4297vl, 28 June, 2007, submitted.
8. I. Daubechies, M. Défrise, and C. De-Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, LVII:1413-1457, 2004.
9. G. Davis, S. Mallat, and M. Avellaneda, Adaptive greedy approximations, Journal of Constructive Approximation, 13:57-98, 1997.
10. G. Davis, S. Mallat, and Z. Zhang, Adaptive time-frequency decompositions, Optical-Engineering, 33(7):2183-91, 1994.
11. A. Dempster, N. Laird, D. Rubin, Maximum likelihood estimation from incomplete data via the EM algorithm, J. Roy. Statist. Soc. B, 39:1-38, 1977.
12. R.A. DeVore, B. Jawerth, and B.J. Lucier, Image compression through wavelet transform coding, IEEE Trans. Information Theory, 38(2):719-746, 1992.
13. D.L. Donoho, De-noising by soft thresholding, IEEE Trans. on Information Theory, 41(3):613-627, 1995.
14. D.L. Donoho, Compressed sensing, IEEE Trans. on Information Theory, 52(4): 1289-306, April 2006.
15. D.L. Donoho and M. Elad, Optimally sparse representation in general (non-orthogonal) dictionaries via U minimization, Proc. of the National Academy of Sciences, 100(5):2197-2202, 2003.
16. D.L. Donoho and M. Elad, On the stability of the basis pursuit in the presence of noise, Signal Processing, 86(3):511-532, March 2006.
17. D.L. Donoho, M. Elad, and V. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Trans. on Information Theory, 52(1):6-18, 2006.
18. D.L. Donoho and I.M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 81(3):425-455, 1994.
19. D.L. Donoho, V. Stodden, and Y. Tsaig, About SparseLab, Stanford University, http://sparselab.stanford.edu, Version 2.0, March, 2007.
20. D.L. Donoho, Y. Tsaig, I. Drori, and J.-L. Starek, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit, submitted to IEEE Trans. on Signal Processing.
21. B. Efron, T. Hastie, I.M. Johnstone, and R. Tibshirani, Least angle regression, The Annals of Statistics, 32(2):407-499, 2004.
22. M. Elad, Why simple shrinkage is still relevant for redundant representations?, to appear in the IEEE Trans. on Information Theory.
23. M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans. on Image Processing 15(12):3736-3745, December 2006.
24. M. Elad, B. Matalon, and M. Zibulevsky, Image denoising with shrinkage and redundant representations, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), NY, June 17-22, 2006.
25. M. Elad, B. Matalon, and M. Zibulevsky, Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization, to appear in Applied and Computational Harmonic Analysis.
26. M. Elad, J.-L. Starek, P. Querre, and D.L. Donoho, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA), Journal on Applied and Comp. Harmonic Analysis, 19:340-358, 2005.
27. M.J. Fadili and J.L. Starek, Sparse representation-based image deconvolution by iterative thresholding, Astronomical Data Analysis ADA'06, Marseille, France, September, 2006.
28. M.A. Figueiredo and R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Processing, 12(8):906-916, 2003.
29. M.A. Figueiredo, and R.D. Nowak, A bound optimization approach to wavelet-based image deconvolution, IEEE International Conference on Image Processing - ICIP 2005, Genoa, Italy, 2:782-785, September 2005.
30. M.A. Figueiredo, J.M. Bioucas-Dias, and R.D. Nowak, Majorization- minimization algorithms for waveletbased image restoration, to appear in the IEEE Trans. on Image Processing.
31. M. Figueiredo, R. Nowak, and S. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems, submitted, 2007.
32. I.F. Gorodnitsky and B.D. Rao, Sparse signal reconstruction from limited data using FOCUSS: A reweighted norm minimization algorithm, IEEE Trans. on Signal Processing, 45(3):600-616, 1997.
33. Y. Hel-Or and D. Shaked, A Discriminative approach for Wavelet shrinkage denoising submitted to the IEEE Trans. on Image Processing.
34. K.K. Herrity, A..C. Gilbert, and J.A. Tropp, Sparse approximation via iterative thresholding, IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), 2006.
35. D. Hunter, K. Lange, A tutorial on MM algorithms, Amer. Statist., 58:30-37, 2004.
36. 1-regularized least squares problems with applications in signal processing and statistics, submitted.
37. N.G. Kingsbury and T.H. Reeves, Overcomplete image coding using iterative projection-based noise shaping, International Conf. on Image Processing (ICIP) (3):597-600, 2002.
38. K. Lange, D.R. Hunter, I. Yang, Optimization transfer using surrogate objective functions (with discussion), J. Comput. Graph. Statist, 9(1): 1-59, 2000.
39. I. Loris, G. Nolet, I. Daubechies, and F.A. Dahlen, Tomographic inversion using l1-norm regularization of wavelet coefficients, arXiv:physics/0608094v1, 8 August, 2006, submitted.
40. M. Lustig, D.L. Donoho, and J.M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, submitted to Magnetic Resonance in Medicine.
41. J. Mairal, M. Elad, and G. Sapiro, Sparse representation for color image restoration, submitted to the IEEE Trans. on Image Processing.
42. S. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Processing, 41(12):3397-3415, 1993.
43. P. Moulin and J. Liu, Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors, IEEE Trans. on Information Theory, 45(3):909-919, 1999.
44. G. Narkiss and M. Zibulevsky, Sequential subspace optimization method for large-scale unconstrained optimization, technical report CCIT No. 559, Technion, The Israel Institute of Technology, Haifa, 2005.
45. R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14(5): 877-898, 1976.
46. S. Sardy, A.G. Bruce, and P. Tseng, Block coordinate relaxation methods for nonparametric signal denoising with wavelet dictionaries, Journal of computational and Graphical Statistics, 9:361-379, 2000.
47. E.P. Simoncelli and E.H. Adelson, Noise removal via Bayesian wavelet coring, Proceedings of the International Conference on Image Processing, Laussanne, Switzerland. September 1996.
48. J.-L. Starek, E.J. Candes, and D.L. Donoho, The curvelet transform for image denoising, IEEE Trans. on Image Processing, 11:670-684, 2002.
49. J.-L. Starek, M. Elad, and D.L. Donoho, Redundant multiscale transforms and their application for morphological component separation, Advances in Imaging And Electron Physics, 132:287-348, 2004.
50. J.-L. Starek, M. Elad, and D.L. Donoho, Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans. on Image Processing, 14(10): 1570-1582, 2005.
51. J.A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. on Information Theory, 50(10):2231-2242, October 2004.
52. J. A. Tropp, Just relax: Convex programming methods for subset selection and sparse approximation, IEEE Trans. on Information Theory, 52(3):1030-1051, March 2006.
53. Y. Tsaig, Sparse Solution Of Underdetermined Linear Systems - Algorithms And Applications, PhD thesis, Stanford, 2007.