Analysis of approximate message passing algorithm

2010 44th Annual Conference on Information Sciences and Systems, CISS 2010

Volumn , Issue , 2010, Pages

  Maleki, Arian ^a   Montanari, Andrea ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC PERFORMANCE; BIPARTITE GRAPHS; COMPRESSED SENSING; FAST RECOVERY; GREEDY METHOD; HOMOTOPIES; INTERIOR POINT METHODS; ITERATIVE THRESHOLDING; MAX-MIN; MESSAGE PASSING ALGORITHM; OPTIMAL THRESHOLDING; PROBLEM SIZE; SOFT-THRESHOLDING ALGORITHM; STATISTICAL PROPERTIES; THEORETICAL FRAMEWORK; THRESHOLDING;

COMPUTATIONAL COMPLEXITY; GRAPH THEORY; INFORMATION SCIENCE; MESSAGE PASSING; METAL RECOVERY; OPTIMIZATION; PHASE TRANSITIONS;

ALGORITHMS;

EID: 77953720142     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CISS.2010.5464887     Document Type: Conference Paper

References (34)

1. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression," Annals of Statistics, vol. 32, pp. 407-499, 2004.
2. A. Maleki and D. L. Donoho, "Optimally tuned iterative thresholding algorithm for compressed sensing," IEEE journal on selected areas in signal processing, 2009. submitted.
3. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," Proceedings of National Academy of Sciences, vol. 106, Nov. 2009.
4. D. L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, vol. 52, pp. 489-509, April 2006.
5. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, vol. 52, pp. 489-509, February 2006.
6. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Journal on Scientific Computing, vol. 20, pp. 33-61, 1998.
7. I. Daubechies, M. Defrise, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Communications on Pure and Applied Mathematics, vol. 75, pp. 1412-1457, 2004.
8. J. L. Starck, M. Elad, and D. L. Donoho, "Redundant multiscale transforms and their application for morphological component analysis," Journal of Advances in Imaging and Electron Physics, vol. 132, pp. 287-348, 2004.
9. P. L. Combettes and V. R. Wajs, "Signal recovery by proximal forward-backward splitting," Multiscale Modeling and Simulation, vol. 4, no. 4, pp. 1168-1200, 2005.
10. K. K. Herrity, A. C. Gilbert, and J. A. Tropp, "Sparse approximation via iterative thresholding," Proc. ICASSP, vol. 3, pp. 624-627, May 2006.
11. D. L. Donoho, I. Drori, Y. Tsaig, and J. L. Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," Stanford Statistics Department Technical Report, 2006.
12. M. Fornasier and H. Rauhut, "Iterative thresholding algorithms," Applied and Computational Harmonic Analysis, vol. 25, no. 2, pp. 187-208, 2008.
13. T. Blumensath and M. E. Davies, "Iterative thresholding for sparse approximations," Journal of Fourier Analysis and Applications, special issue on sparsity, vol. 14, no. 5, pp. 629-654, 2008.
14. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Applied and Computational Harmonic Analysis, vol. 27, no. 3, pp. 265-274, 2009.
15. 1-minimization with applications to compressed sensing," SIAM Journal on Imaging Sciences, vol. 1, no. 1, pp. 143-168, 2008.
16. D. L. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Transactions on Information Theory, vol. 52, pp. 6-18, January 2006.
17. E. Candès, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, vol. 346, pp. 589-592, 2008.
18. D. L. Donoho and J. Tanner, "Neighborliness of randomly-projected simplices in high dimensions," Proceedings of the National Academy of Sciences, vol. 102, no. 27, pp. 9452-9457, 2005.
19. D. L. Donoho and J. Tanner, "Counting faces of randomly projected polytopes when the projection radically lowers dimension," Journal of American Mathematical Society, vol. 22, pp. 1-53, 2009.
20. D. Donoho and J. Tanner, "Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing," Phil. Trans. A, 2009.
21. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655-4666, 2007.
22. 1-norm minimization problems when the solution may be sparse," IEEE Transactions on Information Theory, vol. 54, pp. 4789-4812, November 2008.
23. A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin, "One sketch for all: fast algorithms for compressed sensing," Proc. STOC, pp. 237-246, 2007.
24. D. L. Donoho, "High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension," Discrete and Computational Geometry, vol. 35, no. 4, pp. 617-652, 2006.
25. D. L. Donoho and J. Tanner, "Observed universality of phase transitions in high-dimensional geometry, with applications in modern signal processing and data analysis," Philosophical Transactions of the Royal Society A, vol. 367, no. 1906, pp. 4273-4293, 2009.
26. D. Donoho, I. Johnstone, J. Hoch, and A. Stern, "Maximum entropy and the nearly black object," Journal of the Royal Statistical Society, Series B (Methodological), vol. 54, no. 1, pp. 41-81, 1992.
27. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage.," Biometrika, vol. 81, pp. 425-455, 1994.
28. A. Maleki and A. Montanari, "Analysis of approximate message passing algorithm," Proc. of Conf. Inform. Sci. Sys., 2010. Full version. To be submitted on arXiv.
29. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, Massachussetts: MIT Press, 1963. Available online at http://web./gallager/www/ pages/ldpc.pdf.
30. T. J. Richardson and R. Urbanke, Modern Coding Theory. Cambridge: Cambridge University Press, 2008. Available online at http://lthcwww.epfl.ch/ mct/index.php.
31. T. J. Richardson and R. Urbanke, "The capacity of low-density parity check codes under message-passing decoding," IEEE Trans. Inform. Theory, vol. 47, pp. 599-618, 2001.
32. S. Sarvotham, D. Baron, and R. Baraniuk, "Compressed sensing reconstruction via belief propagation." Preprint, 2006.
33. A. M. D. L. Donoho, A. Maleki, "Message passing algorithms for compressed sensing: I. motivation and construction," Proc. of Information Theory Workshop, 2010.
34. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," Proceedings of National Academy of Sciences, vol. 106, Nov. 2009. Supplement Information.