Model-based compressive sensing

IEEE Transactions on Information Theory

Volumn 56, Issue 4, 2010, Pages 1982-2001

  Baraniuk, Richard G ^a   Cevher, Volkan ^a,b   Duarte, Marco F ^c   Hegde, Chinmay ^a  

^a RICE UNIVERSITY   (United States)

^b EPFL   (Switzerland)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

Block sparsity; Compressive sensing; Signal model; Sparsity; Union of subspaces; Wavelet tree

Indexed keywords

CONVENTIONAL THEORY; GREEDY ALGORITHMS; INNER PRODUCT; MODEL-BASED; NEW THEORY; NUMERICAL SIMULATION; PERFORMANCE GUARANTEES; PERIODIC SAMPLES; RANDOM VECTORS; RECOVERY ALGORITHMS; ROBUST SIGNALS; SENSING SIGNALS; SIGNAL MODELS; SIGNAL RECOVERY; SUFFICIENT CONDITIONS; TWO-STATE; WAVELET TREE;

ALGORITHMS; AMPLIFICATION; COMPUTER SIMULATION;

SIGNAL RECONSTRUCTION;

EID: 77950244328     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2040894     Document Type: Article

References (49)

1. S. Mallat, AWavelet Tour of Signal Processing. San Diego, CA: Academic, 1999.
2. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Sep. 2006.
3. E. J. Candès, "Compressive sampling," in Proc. Int. Congr. Math., Madrid, Spain, 2006, vol.3, pp. 1433-1452.
4. R. G. Baraniuk, "Compressive sensing," IEEE Signal Processing Mag., vol.24, no.4, pp. 118-120, Jul. 2007, 124.
5. V. Cevher,M. F. Duarte, C. Hegde, and R. G. Baraniuk, "Sparse signal recovery using Markov random fields," in Proc. Workshop Neural Inf. Proc. Syst. (NIPS), Vancouver, BC, Canada, Dec. 2008.
6. T. Blumensath and M. E. Davies, "Sampling theorems for signals from the union of finite-dimensional linear subspaces," IEEE Trans. Inf. Theory, vol.55, no.4, pp. 1872-1882, Apr. 2009.
7. Y. M. Lu and M. N. Do, "Sampling signals from a union of subspaces," IEEE Signal Processing Mag., vol.25, no.2, pp. 41-47, Mar. 2008.
8. M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Processing, vol.57, no.8, pp. 3075-3085, Aug. 2009.
9. Y. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11, pp. 5302-5316, Nov. 2009.
10. D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, "Distributed Compressive Sensing," 2005, Preprint.
11. D. Needell and J. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Computat. Harmon. Anal., vol.26, no.3, pp. 301-321, May 2009.
12. M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for waveletbased image restoration," IEEE Trans. Image Processing, vol.12, no.8, pp. 906-916, 2003.
13. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol.57, pp. 1413-1457, 2004.
14. E. J. Candès and J. K. Romberg, "Signal recovery from random projections," in Proc. Computat. Imaging III at SPIE Electron. Imaging, San Jose, CA, Jan. 2005, vol.5674, pp. 76-86.
15. T. Blumensath and M. E. Davies, "Iterative threhsolding for sparse approximations," J. Fourier Anal. Applicat., vol.14, no.5, pp. 629-654, Dec. 2008.
16. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Appl. Computat. Harmon. Anal., vol.27, no.3, pp. 265-274, Nov. 2009.
17. M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol.46, no.4, pp. 886-902, Apr. 1998.
18. R. G. Baraniuk, "Fast reconstruction from incoherent projections," in Workshop Sparse Represent. Redund. Syst., May 2005.
19. M. F. Duarte, M. B.Wakin, and R. G. Baraniuk, "Fast reconstruction of piecewise smooth signals from random projections," in Proc. SPARS05, Rennes, France, Nov. 2005.
20. C. La and M. N. Do, "Tree-based orthogonal matching pursuit algorithm for signal reconstruction," in Proc. IEEE Int. Conf. Image Processing (ICIP), Atlanta, GA, Oct. 2006, pp. 1277-1280.
21. M. F. Duarte, M. B.Wakin, and R. G. Baraniuk,"Wavelet-domain compressive signal reconstruction using a hidden Markov tree model," in Proc. IEEE Int. Conf. Acoust., Speech Signal Processing (ICASSP), Las Vegas, NV, Apr. 2008, pp. 5137-5140.
22. M. N. Do and C. N. H. La, "Tree-based majorize-minimize algorithm for compressed sensing with sparse-tree prior," in Proc. Int. Workshop Computat. Adv. Multi-Sensor Adapt. Processing, St. Thomas, U.S. Virgin Islands, Dec. 2007, pp. 129-132.
23. L. He and L. Carin, "Exploiting structure in wavelet-based Bayesian compressive sensing," IEEE Trans. Signal Processing, vol.57, no.9, pp. 3488-3497, Sep. 2009.
24. K. Lee and Y. Bresler, "Selecting good Fourier measurements for compressed sensing," in SIAM Conf. Imag. Sci., Jul. 2008.
25. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, "Uniform uncertainty principle for Bernoulli and subgaussian ensembles," Constr. Approx., vol.28, no.3, pp. 277-289, Dec. 2008.
26. B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Computat., vol.24, no.2, pp. 227-234, Apr. 1995.
27. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, p. 33, 1998.
28. J. Haupt and R. Nowak, "Signal reconstruction from noisy random projections," IEEE Trans. Inf. Theory, vol.52, no.9, pp. 4036-4048, Sept. 2006.
29. E. J. Candès and T. Tao, "The Dantzig selector: Statistical estimation when is much larger than ." Ann. Stat., vol.35, no.6, pp. 2313-2351, Dec. 2007.
30. J. Tropp and A. C. Gilbert, "Signal recovery from partial information via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol.53, no.12, pp. 4655-4666, Dec. 2007.
31. D. L. Donoho, I. Drori, Y. Tsaig, and J. L. Starck, "Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit," 2006, Preprint.
32. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing: Closing the gap between performance and complexity," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2230-2249, May 2009.
33. E. J. Candès, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, Series I, vol.346, no.9-10, pp. 589-592, May 2008.
34. R. G. Baraniuk and D. L. Jones, "A signal-dependent time-frequency representation: Fast algorithm for optimal kernel design," IEEE Trans. Signal Processing, vol.42, no.1, pp. 134-146, Jan. 1994.
35. R. G. Baraniuk, "Optimal tree approximation with wavelets," in Proc. SPIE Wavelet Applicat. Signal Image Processing VII, Denver, CO, Jul. 1999, vol.3813, pp. 196-207.
36. R. G. Baraniuk, R. A. DeVore, G. Kyriazis, and X. M. Yu, "Near best tree approximation," Adv. Computat. Math., vol.16, no.4, pp. 357-373, May 2002.
37. J. K. Romberg, H. Choi, and R. G. Baraniuk, "Bayesian tree-structured image modeling using wavelet-domain hidden Markov models," IEEE Trans. Image Processing, vol.10, no.7, pp. 1056-1068, July 2001.
38. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using a scale mixture of Gaussians in the wavelet domain," IEEE Trans. Image Processing, vol.12, no.11, pp. 1338-1351, Nov. 2003.
39. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Processing, vol.41, no.12, pp. 3445-3462, Dec. 1993.
40. A. Cohen, W. Dahmen, I. Daubechies, and R. A. DeVore, "Tree approximation and optimal encoding," Appl. Computat. Harmon. Anal., vol.11, no.2, pp. 192-226, Sep. 2001.
41. D. Donoho, "CART and best ortho-basis: A connection," Ann. Stat., vol.25, no.5, pp. 1870-1911, Oct. 1997.
42. M. B. Wakin, S. Sarvotham, M. F. Duarte, D. Baron, and R. G. Baraniuk, "Recovery of jointly sparse signals from few random projections," in Proc. Workshop Neural Inf. Proc. Syst. (NIPS), Vancouver, BC, Canada, Nov. 2005.
43. J. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Processing, vol.86, no.3, pp. 572-588, Apr. 2006.
44. M. F. Duarte, V. Cevher, and R. G. Baraniuk, "Model-based compressive sensing for signal ensembles," in Proc. Allerton Conf. Commun., Contr., Comput., Monticello, IL, Oct. 2009.
45. C. Hegde, M. F. Duarte, and V. Cevher, "Compressive sensing recovery of spike trains using a structured sparsity model," in Proc.Workshop Signal ProcessingWith Adapt. Sparse Structured Representations (SPARS), Saint Malo, France, Apr. 2009.
46. V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, "Recovery of clustered sparse signals from compressive measurements," in Proc. Int. Conf. Sampling Theory Applicat. (SAMPTA), Marseille, France, May 2009.
47. E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, pp. 4203-4215, Dec. 2005.
48. M. Ledoux, The Concentration of Measure Phenomenon. New York: American Mathematical Society, 2001.
49. G. G. Brown and B. O. Shubert, "On random binary trees," Math. Oper. Res., vol.9, no.1, pp. 43-65, Feb. 1984.