Sparse recovery of streaming signals using l1-homotopy

IEEE Transactions on Signal Processing

Volumn 62, Issue 16, 2014, Pages 4209-4223

  Asif, M Salman ^a   Romberg, Justin ^b  

^a Rice University   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Basis pursuit denoising; compressed sensing; Kalman filter; lapped transform; Lasso

Indexed keywords

COMPRESSED SENSING; ITERATIVE METHODS; KALMAN FILTERS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

BASIS PURSUIT DENOISING; LAPPED ORTHOGONAL TRANSFORM; LAPPED TRANSFORM; LASSO; MINIMIZATION PROBLEMS; NUMERICAL EXPERIMENTS; RECONSTRUCTION FRAMEWORKS; WEIGHTED L;

RECOVERY;

EID: 84904994734     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2014.2328981     Document Type: Article

References (53)

1. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
2. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
3. E. Candès, "Compressive sampling," in Proc. Int. Congr. Mathematicians, Madrid, Spain, vol. 3, pp. 1433-1452.
4. R. Baraniuk, V. Cevher, M. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory, vol. 56, no. 4, pp. 1982-2001, Apr. 2010.
5. B. Olshausen and D. Field, "Sparse coding with an overcomplete basis set: A strategy employed by V1?," Vision Res., vol. 37, no. 23, pp. 3311-3325, 1997. (Pubitemid 27493805)
6. K. Kreutz-Delgado, J. Murray, B. Rao, K. Engan, T. Lee, and T. Sejnowski, "Dictionary learning algorithms for sparse representation," Neural Comput., vol. 15, no. 2, pp. 349-396, 2003. (Pubitemid 37049825)
7. M. Lustig, D. Donoho, J. Santos, and J. Pauly, "Compressed Sensing MRI [A look at how CS can improve on current imaging techniques]," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72-82, Mar. 2008. (Pubitemid 351513068)
8. M. S. Lewicki and T. J. Sejnowski, "Coding time-varying signals using sparse, shift-invariant representations," in Advances in Neural Information Processing Systems 11. Cambridge, MA, USA: MIT Press, 1999, pp. 730-736.
9. W. Li and J. Preisig, "Estimation of rapidly time-varying sparse channels," IEEE J. Ocean. Eng., vol. 32, no. 4, pp. 927-939, 2007. (Pubitemid 351385394)
10. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc., Series B, vol. 58, no. 1, pp. 267-288, 1996.
11. S. S. Chen, D. L. Donoho, and M.A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1999. (Pubitemid 128689501)
12. E. Candès and T. Tao, "The Dantzig selector: Statistical estimation when is much larger than," Ann. Statist., vol. 35, no. 6, pp. 2313-2351, 2007.
13. M. S. Asif, D. Reddy, P. T. Boufounos, and A. Veeraraghavan, "Streaming compressive sensing for high-speed periodic videos," in Proc. 17th IEEE Int. Conf. Image Process. (ICIP), 2010, pp. 3373-3376.
14. P. T. Boufounos and M. S. Asif, "Compressive sampling for streaming signals with sparse frequency content," in Proc. 44th Annu. Conf. Inf. Sci. Syst. (CISS), Princeton, NJ, USA, Mar. 2010.
15. H. Zou, "The adaptive lasso and its oracle properties," J. Amer. Statist. Assoc., vol. 101, no. 476, pp. 1418-1429, 2006.
16. E. J. Candès, M. B. Wakin, and S. P. Boyd, "Enhancing sparsity by reweighted minimization," J. Fourier Anal. Appl., vol. 14, no. 5-6, pp. 877-905, 2008.
17. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, Mar. 2004.
18. S. Wright, R. Nowak, and M. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process., vol. 57, no. 7, pp. 2479-2493, Jul. 2009.
19. J. Yang and Y. Zhang, "Alternating direction algorithms for -problems in compressive sensing," SIAM J. Sci. Comput., vol. 33, no. 1-2, pp. 250-278, 2011.
20. S. Becker, J. Bobin, and E. Candès, "NESTA: A fast and accurate firstorder method for sparse recovery," SIAM J. Imag. Sci., vol. 4, no. 1, pp. 1-39, 2011.
21. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 183-202, 2009.
22. H. Malvar and D. Staelin, "The LOT: Transform coding without blocking effects," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 4, pp. 553-559, 1989.
23. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York, NY, USA: Academic Press, 1999.
24. M. Osborne, B. Presnell, and B. Turlach, "A new approach to variable selection in least squares problems," IMA J. Numer. Anal., vol. 20, no. 3, pp. 389-403, 2000.
25. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression," Ann. Statist., vol. 32, no. 2, pp. 407-499, 2004. (Pubitemid 41250302)
26. P. Garrigues and L. E. Ghaoui, "An homotopy algorithm for the lasso with online observations," Adv. Neural Inf. Process. Syst., vol. 21, pp. 489-496, 2008.
27. M. S. Asif and J. Romberg, "Streaming measurements in compressive sensing: filtering," in Proc. 42nd Asilomar Conf. Signals, Syst., Comput., Oct. 2008, pp. 1051-1058.
28. M. S. Asif and J. Romberg, "Dynamic updating for sparse time varying signals," in Proc. 43rd Annu. Conf. Inf. Sci. Syst. (CISS), Mar. 2009, pp. 3-8.
29. M. S. Asif and J. Romberg, "Dynamic updating for minimization," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 421-434, Apr. 2010.
30. M. S. Asif and J. Romberg, "Sparse signal recovery and dynamic update of the underdetermined system," in Proc. 44th Asilomar Conf. Signals, Syst., Comput., Nov. 2010, pp. 798-802.
31. T.-J. Yang, Y.-M. Tsai, C.-T. Li, and L.-G. Chen, "WarmL1: A warmstart homotopy-based reconstruction algorithm for sparse signals," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jul. 2012, pp. 2226-2230.
32. M. S. Asif and J. Romberg, "Fast and accurate algorithms for re-weighted -norm minimization," IEEE Trans. Signal Process., vol. 61, no. 23, pp. 5905-5916, 2013.
33. G. Golub and C. Van Loan, Matrix Computations. Baltimore, MD, USA: The Johns Hopkins Univ. Press, 1996.
34. R. Kalman, "A new approach to linear filtering and prediction problems," J. Basic Eng., vol. 82, no. 1, pp. 35-45, 1960.
35. H. W. Sorenson, "Least-squares estimation: From Gauss to Kalman," IEEE Spectrum, vol. 7, no. 7, pp. 63-68, 1970.
36. T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation. Upper Saddle River, NJ, USA: Prentice-Hall, 2000.
37. P. T. Boufounos and M. S. Asif, "Compressive sensing for streaming signals using the streaming greedy pursuit," in Proc. MILCOM, Nov. 2010, pp. 1205-1210.
38. D. Needell and J. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples.," Appl. Comput. Harmon. Anal., vol. 26, pp. 301-321, June 2008.
39. S. Pudlewski and T. Melodia, "A tutorial on encoding and wireless transmission of compressively sampled videos," IEEE Commun. Surveys Tuts., vol. 15, no. 2, pp. 754-767, 2013.
40. N. Vaswani, "Kalman filtered compressed sensing," in Proc. 15th IEEE Int. Conf. Image Process., Oct. 2008, pp. 893-896.
41. A. Carmi, P. Gurfil, and D. Kanevsky, "Methods for sparse signal recovery using Kalman filtering pseudo-measurement norms and quasinorms," IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2405-2409, Apr. 2010.
42. D. Angelosante, S. I. Roumeliotis, and G. B. Giannakis, "Lasso- Kalman smoother for tracking sparse signals," in Proc. 43rd Asilomar Conf. Signals, Syst., Comput., Nov. 2009, pp. 181-185.
43. A. Charles, M. S. Asif, J. Romberg, and C. Rozell, "Sparsity penalties in dynamical system estimation," in Proc. Conf. Inf. Syst. Sci. (CISS), Mar. 2011.
44. M. S. Asif, A. Charles, J. Romberg, and C. Rozell, "Estimation and dynamic updating of time-varying signals with sparse variations," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), May 2011, pp. 3908-3911.
45. J. Ziniel, L. C. Potter, and P. Schniter, "Tracking and smoothing of time-varying sparse signals via approximate belief propagation," in Proc. 44th Asilomar Conf. Signals, Syst., Comput., Nov. 2010, pp. 808-812.
46. M. S. Asif, L. Hamilton, M. Brummer, and J. Romberg, "Motion- adaptive spatio-temporal regularization for accelerated dynamic MRI," Magn. Reson. Med., vol. 70, no. 3, pp. 800-812, 2013.
47. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding. Englewood Cliffs, NJ, USA: Prentice Hall PTR, 1995.
48. R. T. Rockafellar, Convex Analysis. Princeton, NJ, USA: Princeton Univ. Press, 1997.
49. D. L. Donoho and Y. Tsaig, "Fast solution of -norm minimization problems when the solution may be sparse," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 4789-4812, 2008.
50. M. S. Asif, "Dynamic compressive sensing: Sparse recovery algorithms for streaming signals and video," Ph.D. dissertation, Georgia Inst. of Technol., Atlanta, GA, USA, 2013.
51. Å. Björck, Numerical Methods for Least Squares Problems. Philadelphia, PA, USA: SIAM, 1996.
52. J. Buckheit, S. Chen, D. Donoho, and I. Johnstone, Wavelab 850, Software Toolbox [Online]. Available: http://www-stat.stanford. edu/~wavelab/
53. A. Cohen, I. Daubechies, and J.-C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math., vol. 45, no. 5, pp. 485-560, 1992.