Sparse component analysis

Handbook of Blind Source Separation

Volumn , Issue , 2010, Pages 367-420

  Gribonval, R ^a   Zibulevsky, M ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874127157     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-12-374726-6.00015-1     Document Type: Chapter

References (117)

1. S. Abdallah, M. Plumbley, If edges are the independent components of natural images, what are the independent components of natural sounds? in: Proc. Int. Conf. Indep. Component Anal. and Blind Signal Separation, ICA2001, San Diego, California, December 2001, pp. 534-539.
2. Abrard F., Deville Y. A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources. Signal Processing 2005, 85:1389-1403.
3. F. Abrard, Y. Deville, P. White, From blind source separation to blind source cancellation in the underdetermined case: a new approach based on time-frequency analysis, in: Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation, ICA 2001, San Diego, California, December 2001.
4. Aharon M., Elad M., Bruckstein A. The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing 2006, 54:4311-4322.
5. Aharon M., Elad M., Bruckstein A. On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them. Journal of Linear Algebra and Applications 2006, 416:48-67.
6. A. Aïssa-El-Bey, K. Abed-Meraim, Y. Grenier, Underdetermined blind source separation of audio sources in time-frequency domain, in: Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005.
7. Amari S., Cichocki A., Yang H.H. A new learning algorithm for blind signal separation. Advances in Neural Information Processing Systems 1996, vol. 8. MIT Press.
8. Arberet S., Gribonval R., Bimbot F. A robust method to count and locate audio sources in a stereophonic linear instantaneous mixture. LNCS Series March 2006, vol. 3889:536-543. Springer. J.P. Rosca, D. Erdogmus, S. Haykin (Eds.).
9. R. Balan, J. Rosca, Statistical properties of STFT ratios for two channel systems and applications to blind source separation, in: Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation, ICA 2000, Helsinki, Finland, June 2000, pp. 429-434.
10. Ben-Tal A., Zibulevsky M. Penalty/barrier multiplier methods for convex programming problems. SIAM Journal on Optimization 1997, 7:347-366.
11. Bertsekas D. Constrained Optimization and Lagrange Multiplier Methods 1982, Academic Press, New York.
12. Bertsekas D. Non-Linear Programming 1995, Athena Scientific, Belmont, MA. 2nd ed.
13. J. Bobin, Y. Moudden, J.-L. Starck, M. Elad, Multichannel morphological component analysis, in: Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005.
14. Bobin J., Starc J.-L., Fadili J., Moudden Y., Donoho D.L. Morphological component analysis: An adaptative thresholding strategy. IEEE Transactions on Image Processing 2007, 16:2675-2681.
15. Bofill P., Zibulevsky M. Underdetermined blind source separation using sparse representations. Signal Processing 2001, 81:2353-2362.
16. Bronstein A.M., Bronstein M.M., Zibulevsky M. Blind source separation using block-coordinate relative Newton method. Signal Processing 2004, 84:1447-1459.
17. Bronstein A.M., Bronstein M.M., Zibulevsky M. Relative optimization for blind deconvolution. IEEE Transactions on Signal Processing 2005, 53:2018-2026.
18. Bronstein A.M., Bronstein M.M., Zibulevsky M., Zeevi Y.Y. Blind deconvolution of images using optimal sparse representations. IEEE Transactions on Image Processing 2005, 14:726-736.
19. Cardoso J.-F. Blind signal separation: Statistical principles. Proceedings of the IEEE 1998, 9:2009-2025. Special Issue on Blind Identification and Estimation.
20. Cardoso J.-F. High-order contrasts for independent component analysis. Neural Computation 1999, 11:157-192.
21. J.-F. Cardoso, JADE for real-valued data, tech. report, ENST, 1999. http://sig.enst.fr:80/~cardoso/guidesepsou.html.
22. Cardoso J.-F., Laheld B. Equivariant adaptive source separation. IEEE Transactions on Signal Processing 1996, 44:3017-3030.
23. Chen S.S., Donoho D.L., Saunders M.A. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 1998, 20:33-61.
24. A. Cichocki, S. Amari, K. Siwek, ICALAB toolbox for image processing-benchmarks, tech. report, The Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, 2002. http://www.bsp.brain.riken.go.jp/ICALAB/ICALABImageProc/benchmarks/.
25. Cichocki A., Unbehauen R., Rummert E. Robust learning algorithm for blind separation of signals. Electronics Letters 1994, 30:1386-1387.
26. Coifman R.R., Meyer Y., Wickerhauser M.V. Wavelet analysis and signal processing. Wavelets and their Applications 1992, Jones and Barlett, Boston. B. Ruskai (Ed.).
27. Cotter S., Rao B., Engan K., Kreutz-Delgado K. Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Transactions on Signal Processing 2005, 53:2477-2488.
28. Daubechies I., Defrise M., De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics 2004, 57:1413-1457.
29. Daudet L., Torrésani B. Hybrid representations for audiophonic signal encoding. Signal Processing 2002, 82:1595-1617. Special Issue on Coding Beyond Standards.
30. Davies M., Mitianoudis N. A sparse mixture model for overcomplete ICA. IEE Proceedings-Vision Image and Signal Processing 2004, 151:35-43. Special issue on Nonlinear and Non-Gaussian Signal Processing.
31. Davis G., Mallat S., Avellaneda M. Adaptive greedy approximations. Construction Approximation 1997, 13:57-98.
32. Donoho D., Elad M., Temlyakov V. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory 2006, 52:6-18.
33. Donoho D., Huo X. Uncertainty principles and ideal atomic decompositions. IEEE Transactions on Information Theory 2001, 47:2845-2862.
34. C. Dossal, Estimation de fonctions géométriques et déconvolution, PhD thesis, École Polytechnique, Palaiseau, France, 2005.
35. Efron B., Hastie T., Johnstone I., Tibshirani R. Least angle regression. Annals of Statistics 2004, 32:407-499.
36. Elad M. Why simple shrinkage is still relevant for redundant representations?. IEEE Transactions on Information Theory 2006, 52:5559-5569.
37. Elad M., Matalon B., Zibulevsky M. Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization. Applied and Computational Harmonic Analysis 2007, 23:346-367.
38. Abrard Y.F. Blind separation of dependent sources using the "time-frequency ratio of mixtures" approach. ISSPA 2003, IEEE, Paris, France.
39. Févotte C., Doncarli C. Two contributions to blind source separation using time-frequency distributions. IEEE Signal Processing Letters 2004, 11:386-389.
40. Févotte C., Godsill S.J. A Bayesian approach for blind separation of sparse sources. IEEE Transactions on Audio, Speech and Language Processing 2006, 14(6):2174-2188.
41. Field D., Olshausen B. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 1996, 381:607-609.
42. Figueiredo M., Nowak R. An EM algorithm for wavelet-based image restoration. IEEE Transactions on Image Processing 2003, 12:906-916.
43. Figueras i Ventura R.M., Vandergheynst P., Frossard P. Low rate and flexible image coding with redundant representations. IEEE Transactions on Image Processing 2006, 15:726-739.
44. M. Fornasier, H. Rauhut, Recovery algorithms for vector valued data with joint sparsity constraints, Tech. Report 27, Johns Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, 2006.
45. J.-J. Fuchs, Some further results on the recovery algorithms, in: Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005, pp. 67-70.
46. Gill P.E., Murray W., Wright M.H. Practical Optimization 1981, Academic Press, New York.
47. Golub G.H., Van Loan C. Matrix Computations 1989, The Johns Hopkins University Press, Baltimore and London. 2nd ed.
48. Gorodnitsky I.F., Rao B.D. Sparse signal reconstruction from limited data using focuss: A reweighted norm minimization algorithm. IEEE Transactions on Signal Processing 1997, 45:600-616.
49. Gribonval R. Sparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture. Proc. Int. Conf. Acoust. Speech Signal Process. 2002, vol. 3:III/3057-III/3060. IEEE, Orlando, Florida.
50. R. Gribonval, Piecewise linear source separation, in: M. Unser, A. Aldroubi, A. Laine, (Eds.), Proc. SPIE '03, in: Wavelets: Applications in Signal and Image Processing X, vol. 5207, San Diego, CA, August 2003, pp. 297-310.
51. R. Gribonval, L. Benaroya, E. Vincent, C. Févotte, Proposals for performance measurement in source separation, in: Proc. 4th Int. Symp. on Independent Component Anal. and Blind Signal Separation, ICA2003, Nara, Japan, April 2003, pp. 763-768.
52. Gribonval R., Figueras i Ventura R.M., Vandergheynst P. A simple test to check the optimality of sparse signal approximations. EURASIP Signal Processing 2006, 86:496-510. Special issue on Sparse Approximations in Signal and Image Processing.
53. R. Gribonval, S. Krstulović, MPTK, The Matching Pursuit Toolkit, 2005.
54. Gribonval R., Nielsen M. On the strong uniqueness of highly sparse expansions from redundant dictionaries. LNCS 2004, Springer-Verlag, Granada, Spain.
55. Gribonval R., Nielsen M. Highly sparse representations from dictionaries are unique and independent of the sparseness measure. Appl. Comput. Harm. Anal. 2007, 22:335-355.
56. Gribonval R., Nielsen M. Beyond sparsity: Recovering structured representations by ℓ1-minimization and greedy algorithms. Advances in Computational Mathematics 2008, 28:23-41.
57. Gribonval R., Rauhut H., Schnass K., Vandergheynst P. Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms. Journal of Fourier Analysis and Applications 2008, 14:655-687.
58. Gribonval R., Vandergheynst P. On the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries. IEEE Transactions on Information Theory 2006, 52:255-261.
59. A. Hyvärinen, The Fast-ICA MATLAB package, tech. report, HUT, 1998. http://www.cis.hut.fi/~aapo/.
60. Hyvärinen A. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 1999, 10:626-634.
61. A. Jourjine, S. Rickard, O. Yilmaz, Blind separation of disjoint orthogonal signals: Demixing n sources from 2 mixtures, in: Proc. IEEE Conf. Acoustics Speech and Signal Proc., ICASSP'00, vol. 5, Istanbul, Turkey, June 2000, pp. 2985-2988.
62. Kisilev P., Zibulevsky M., Zeevi Y. A multiscale framework for blind separation of linearly mixed signals. The Journal of Machine Learning Research 2003, 4:1339-1363.
63. P. Kisilev, M. Zibulevsky, Y.Y. Zeevi, B.A. Pearlmutter, Multiresolution framework for sparse blind source separation, tech. report, Department of Electrical Engineering, Technion. Haifa, Israel, 2000. http://ie.technion.ac.il/~mcib/.
64. Kreutz-Delgado K., Rao B., Engan K., Lee T.-W., Sejnowski T. Convex/schur-convex (csc) log-priors and sparse coding. 6th Joint Symposium on Neural Computation 1999, 65-71. Institute for Neural Computation.
65. S. Krstulovic, R. Gribonval, MPTK: Matching Pursuit made tractable, in: Proc. Int. Conf. Acoust. Speech Signal Process., ICASSP'06, vol. 3, Toulouse, France, May 2006, pp. III-496-III-499.
66. Lee T.-W., Lewicki M.S., Girolami M., Sejnowski T.J. Blind source separation of more sources than mixtures using overcomplete representations. IEEE Signal Processing Letters 1999, 6:87-90.
67. Lesage S., Krstulovic S., Gribonval R. Under-determined source separation: comparison of two approaches based on sparse decompositions. LNCS Series 2006, vol. 3889:633-640. Springer. J.P. Rosca, D. Erdogmus, S. Haykin (Eds.).
68. D. Leviatan, V. Temlyakov, Simultaneous approximation by greedy algorithms, Tech. Report 0302, IMI, Dept. of Mathematics, University of South Carolina, Columbia, SC 29208, 2003.
69. Lewicki M. Efficient coding of natural sounds. Nature Neuroscience 2002, 5:356-363.
70. Lewicki M., Sejnowski T. Learning overcomplete representations. Neural Computation 2000, 12:337-365.
71. Lewicki M.S., Olshausen B.A. A probabilistic framework for the adaptation and comparison of image codes. Journal of the Optical Society of America 1999, 16:1587-1601.
72. Lin J., Grier D., Cowan J. Faithful representation of separable distributions. Neural Computation 1997, 9:1305-1320.
73. S. Makeig, ICA toolbox for psychophysiological research, Computational Neurobiology Laboratory, the Salk Institute for Biological Studies, 1998. http://www.cnl.salk.edu/~ica.html.
74. D. Malioutov, M. Cetin, A. Willsky, Homotopy continuation for sparse signal representation, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP'05, vol. V, March 2005, pp. 733-736.
75. Mallat S. A Wavelet Tour of Signal Processing 1998, Academic Press, San Diego, CA.
76. Mallat S., Zhang Z. Matching pursuit with time-frequency dictionaries. IEEE Transactions on Signal Processing 1993, 41:3397-3415.
77. T. Melia, S. Rickard, Extending the DUET blind source separation technique, in: Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005, pp. 67-70.
78. Natarajan B. Sparse approximate solutions to linear systems. SIAM Journal on Computing 1995, 25:227-234.
79. D. Needell, J.A. Tropp, Cosamp: Iterative signal recovery from incomplete and inaccurate samples, tech. report, Caltech, 2008.
80. Olshausen B.A., Field D.J. Sparse coding with an overcomplete basis set: A strategy employed by v1?. Vision Research 1997, 37:3311-3325.
81. Pearlmutter B.A., Parra L.C. Maximum likelihood blind source separation: A context-sensitive generalization of ICA. Advances in Neural Information Processing Systems 1997, vol. 9. MIT Press.
82. E. Pearson, The Multiresolution Fourier Transform and its application to Polyphonic Audio Analysis, PhD thesis, University of Warwick, September 1991.
83. Peotta L., Granai L., Vandergheynst P. Image compression using an edge adapted redundant dictionary and wavelets. Signal Processing 2006, 86:444-456.
84. Pham D., Garat P. Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach. IEEE Transactions on Signal Processing 1997, 45:1712-1725.
85. M. Plumbley, Geometry and homotopy for ℓ1 sparse signal representations, in Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005, pp. 67-70.
86. Polyak R. Modified barrier functions: Theory and methods. Mathematical Programming 1992, 54:177-222.
87. Princen J., Bradley A. Analysis/synthesis filter bank design bases on time domain aliasing cancellation. IEEE Transactions on Acoustics, Speech and Signal Proc. 1986, ASSP-34:1153-1161.
88. Puigt M., Deville Y. Time-frequency ratio-based blind separation methods for attenuated and time-delayed sources. Mechanical Systems and Signal Processing 2005, 19:1348-1379.
89. Rabiner L., Schafer R. Digital Processing of Speech Signals 1978, Prentice Hall.
90. Rahmoune A V.P., P F. Flexible motion-adaptive video coding with redundant expansions. IEEE Transactions on Circuits and Systems for Video Technology 2006, 16:178-190.
91. S. Rickard, R. Balan, J. Rosca, Real-time time-frequency based blind source separation, in: 3rd International Conference on Independent Component Analysis and Blind Source Separation, ICA2001, San Diego, CA, December 2001.
92. R. Rubinstein, M. Zibulevsky, M. Elad, Double sparsity: Learning sparse dictionaries for sparse signal approximation, IEEE Transactions on Signal Processing (2009) (in press).
93. R. Saab, Ö Yilmaz, M. McKeown, R. Abugharbieh, Underdetermined sparse blind source separation with delays, in Proc. First Workshop on Signal Processing with Sparse/Structured Representations, SPARS'05, Rennes, France, November 2005, pp. 67-70.
94. Santosa F., Symes W. Linear inversion of band-limited reflection sismograms. SIAM J. Sci. Statistic. Comput. 1986, 7:1307-1330.
95. Starck J.L., Candès E.J., Donoho D.L. The curvelet transform for image denoising. IEEE Transactions on Image Processing 2000, 11:670-684.
96. Starck J.-L., Elad M., Donoho D. Image decomposition : Separation of textures from piecewise smooth content. Proc. SPIE '03 August 2003, vol. 5207:571-582. SPIE (The International Society for Optical Engineering), San Diego, CA. M. Unser, A. Aldroubi, A. Laine (Eds.).
97. J.-L. Starck, Y. Moudden, J. Bobin, M. Elad, D. Donoho, Morphological component analysis, in: Proceedings of the SPIE conference wavelets, vol. 5914, July 2005.
98. Theis F., Jung A., Puntonet C., Lang E. Linear geometric ICA: Fundamentals and algorithms. Neural Computation 2003, 15:419-439.
99. F.J. Theis, E.W. Lang, Formalization of the two-step approach to overcomplete BSS, in: Proc. SIP 2002, Kauai, Hawaii, USA, 2002, pp. 207-212.
100. F.J. Theis, C. Puntonet, E.W. Lang, A histogram-based overcomplete ICA algorithm, in: Proc. 4th Int. Symp. on Independent Component Anal. and Blind Signal Separation, ICA2003, Nara, Japan, 2003, pp. 1071-1076.
101. Tropp J. Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Inform. Theory 2004, 50:2231-2242.
102. Tropp J. Algorithms for simultaneous sparse approximation. Part II: Convex relaxation. Signal Processing 2006, 86:589-602. Special issue on Sparse Approximations in Signal and Image Processing.
103. Tropp J. Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Transactions on Information Theory 2006, 52:1030-1051.
104. Tropp J., Gilbert A., Strauss M. Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit. Signal Processing 2006, 86:572-588. Special issue on Sparse Approximations in Signal and Image Processing.
105. B. Turlach, On algorithms for solving least squares problems under an ℓ1 pernalty or an ℓ1 constraint, in: 2004 Proc. of the American Statistical Association, vol. Statistical Computing Section [CDROM] Alexandria, VA, American Statistical Association, 2005, pp. 2572-2577.
106. M. Van Hulle, Clustering approach to square and non-square blind source separation. in: IEEE Workshop on Neural Networks for Signal Processing, NNSP99, 1999, pp. 315-323.
107. L. Vielva, D. Erdogmus, J. Principe, Underdetermined blind source separation using a probabilistic source sparsity model, in: Proc. Int. Conf. on ICA and BSS, ICA2001, San Diego, California, 2001, pp. 675-679.
108. Vincent E. Complex nonconvex lp norm minimization for underdetermined source separation. Proc. Int. Conf. Indep. Component Anal. and Blind Signal Separation 2007, 430-437. Springer.
109. Weitzer D., Stanhill D., Zeevi Y.Y. Nonseparable two-dimensional multiwavelet transform for image coding and compression. Proc. SPIE 1997, 3309:944-954.
110. Xu R., Wunsch II D. Survey of clustering algorithms. IEEE Transactions on Neural Networks 2005, 16:645-678.
111. Yilmaz O., Rickard S. Blind separation of speech mixtures via time-frequency masking. IEEE Transactions on Signal Processing 2004, 52:1830-1847.
112. M. Zibulevsky, Blind source separation with Relative Newton method, Proceedings ICA-2003, (2003), pp. 897-902.
113. Zibulevsky M. Relative Newton and smoothing multiplier optimization methods for blind source separation. Springer Series: Signals and Communication Technology XV 2007, Springer. S. Makino, T. Lee, H. Sawada (Eds.).
114. Zibulevsky M., Kisilev P., Zeevi Y.Y., Pearlmutter B.A. Blind source separation via multinode sparse representation. Advances in Neural Information Processing Systems 2002, vol. 12. MIT Press.
115. Zibulevsky M., Pearlmutter B.A. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 2001, 13:863-882.
116. M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition, Tech. Report CS99-1, Univ. of New Mexico, July 1999.
117. Zibulevsky M., Pearlmutter B.A., Bofill P., Kisilev P. Blind source separation by sparse decomposition. Independent Components Analysis: Principles and Practice 2001, Cambridge University Press. S.J. Roberts, R.M. Everson (Eds.).