Exploiting structure in wavelet-based bayesian compressive sensing

IEEE Transactions on Signal Processing

Volumn 57, Issue 9, 2009, Pages 3488-3497

  He, Lihan ^a   Carin, Lawrence ^a  

^a Duke University   (United States)

Author keywords

Bayesian signal processing; Compression; Sparseness; Wavelets

Indexed keywords

BAYESIAN; BAYESIAN SIGNAL PROCESSING; COMPRESSION; HIERARCHICAL BAYESIAN MODELS; INVERSION ALGORITHM; MARKOV CHAIN MONTE CARLO; NATURAL IMAGES; PERFORMANCE COMPARISON; SPARSENESS; STATISTICAL STRUCTURES; WAVELET BASIS; WAVELET COEFFICIENTS; WAVELET-BASED COMPRESSIONS; WAVELETS;

MARKOV PROCESSES; SIGNAL PROCESSING; SIGNAL RECONSTRUCTION; WAVELET TRANSFORMS;

BAYESIAN NETWORKS;

EID: 69349089478     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2022003     Document Type: Article

References (46)

1. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York: Academic, 1998.
2. G. K. Wallace, "The JPEG still picture compression standard," IEEE Trans. Consumer Electron., vol. 38, pp. 18-34, 1992.
3. C. Christopoulos, "JPEG2000 tutorial," in Proc. IEEE Int. Conf. Image Process. (ICIP), Kobe, Japan, 1999 [Online]. Available: http://www.dsp.toronto.edu/dsp/JPEG2000/
4. 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, pp. 243-250, 1996.
5. M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov model," IEEE Trans. Signal Process., vol. 46, pp. 886-902, 1998.
6. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol. 23, pp. 969-985, 2007.
7. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, pp. 489-509, 2006.
8. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, pp. 1289-1306, 2006.
9. E. J. Candès and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag., vol. 25, pp. 21-30, 2008.
10. M. Lustig, D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Reson. Med., vol. 58, pp. 1182-1195, 2007.
11. A. Wagadarikar, R. John, R. Willett, and D. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt., vol. 47, pp. B44-B51, 2008.
12. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, pp. 4655-4666, 2007.
13. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Computat. Harmon. Analysis Jun. 2008.
14. D. L. Donoho, Y. Tsaig, I. Drori, and J.-L. Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," Stanford Statistics Tech. Rep. 2006-2, Apr. 2006.
15. S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., vol. 56, pp. 2346-2356, 2008.
16. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Scientif. Comput., vol. 20, pp. 33-61, 1999.
17. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression," Ann. Statist. (With Discussion), vol. 32, pp. 407-499, 2004.
18. T. Blumensath and M. E. Davies, "Sampling theorems for signals from the union of linear subspaces," IEEE Trans. Inf. Theory, 2008, submitted for publication.
19. A. Hormati and M. Vetterli, "Annihilating flter-based decoding in the compressed sensing framework," Proc. SPIE Wavelets XII, 2007.
20. Y. C. Eldar and M. Mishali, Robust Recovery of Signals From a Union of Subspaces, 2008, to be published.
21. R. G. Baraniuk, V. Cevher,M. F. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory, 2008, submitted for publication.
22. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using Gaussian scale mixtures in the wavelet domain," IEEE Trans. Image Process., vol. 12, pp. 1338-1351, 2002.
23. J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vision, vol. 40, no. 1, pp. 49-70, 2000.
24. C. La and M. Do, "Signal reconstruction using sparse tree representations," in Proc. SPIE Wavelets XI, 2005.
25. 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 Process. (ICASSP), 2008, pp. 5137-5140.
26. Y. Tsaig and D. L. Donoho, "Extensions of compressed sensing," Signal Process., vol. 86, no. 3, pp. 549-571, 2006.
27. E. J. Candès and J. Romberg, "Practical signal recovery from random projections," in Proc. SPIE Conf. 5914 Wavelet Appl. Signal and Image Process. XI, 2004.
28. J. Duarte-Carvajalino and G. Sapiro, "Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization, " IMA Preprint Series 2211, 2008.
29. G. Peyré, "Best basis compressed sensing," in Proc. Int. Conf. Scale Space Variat. Methods Comput. Vision (SSVM), 2007.
30. M. Seeger and H. Nickisch, "Compressed sensing and Bayesian experimental design," in Proc. 25th Int. Conf. Mach. Learn. (ICML) 2008, pp. 912-919.
31. D. Wipf, J. Palmer, and B. Rao, "Perspectives on sparse Bayesian learning," in Advances in Neural Information Processing Systems 16 Cambridge, MA: MIT Press, 2004.
32. H. Ishwaran and J. S. Rao, "Spike and slab variable selection : Frequentist and Bayesian strategies," Ann. Statist., vol. 33, pp. 730-773, 2005.
33. E. I. George and R. E. McCulloch, "Variable selection via Gibbs sampling," J. Amer. Statist. Assoc., vol. 88, pp. 881-889, 1993.
34. H. Chipman, "Bayesian variable selection with related predictors," Canad. J. Statist., vol. 24, pp. 17-36, 1996.
35. C. Carvalho, J. Chang, J. Lucas, Q. Wang, J. Nevins, and M. West, "High-dimensional sparse factor modelling: Applications in gene expression genomics," J. Amer. Statist. Assoc., 2008.
36. M. West, "Bayesian factor regression models in the large p, small n paradigm," in Bayesian Statist. 7, J. M. Bernardo, A. P. Dawid, J. O. Berger, M. West, D. Heckerman, M. J. Bayarri, and A. F. M. Smith, Eds. Oxford, U.K.: Oxford Univ. Press, 2003, pp. 723-732.
37. J. M. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol. 41, pp. 3445-3462, 1993.
38. T. Blumensath and M. E. Davies, Iterative Hard Thresholding for Compressed Sensing, Jul. 2008, to be published.
39. S. Ray and B. Mallick, "Functional clustering by Bayesian wavelet methods," J. Royal Statist. Soc. Series B, Statist. Methodol., vol. 68, pp. 305-332, 2006.
40. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., pp. 211-244, 2000.
41. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. New York: Springer, 2004.
42. M. J. Beal, "Variational Algorithms for Approximate Bayesian Inference," Ph.D., Gatsby Computational Neuroscience Unit, University College London, London, U.K., 2003.
43. C. Bishop and M. Tipping, "Variational relevance vector machines," in Proc. 16th Ann. Conf. Uncertainty in Artificial Intelligence (UAI) San Francisco, CA, 2000, pp. 46-53.
44. D. Baron, M. B. Wakin, M. F. Duarte, S. Sarvotham, and R. G. Baraniuk, "Distributed compressed sensing," in Proc. 39th Asilomar Conf. Signals, Syst. Comput., 2005, pp. 1537-1541.
45. S. Ji, D. Dunson, and L. Carin, "Multi-task compressive sensing," IEEE Trans. Signal Process., vol. 57, Jan. 2009.
46. Y. Qi, D. Liu, L. Carin, and D. Dunson, "Multi-task compressive sensing with dirichlet process priors," in Proc. Int. Conf. Mach. Learn. (ICML), 2008.