Recovery of sparse translation-invariant signals with continuous basis pursuit

IEEE Transactions on Signal Processing

Volumn 59, Issue 10, 2011, Pages 4735-4744

  Ekanadham, Chaitanya ^a   Tranchina, Daniel ^b   Simoncelli, Eero P ^b,c  

^a NEW YORK UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c HOWARD HUGHES MEDICAL INSTITUTE   (United States)

Author keywords

Basis pursuit; feature decomposition; interpolation; L1 optimization; sparsity; transformation invariance

Indexed keywords

BASIS PURSUITS; FEATURE DECOMPOSITION; L1 OPTIMIZATIONS; SPARSITY; TRANSFORMATION-INVARIANCE;

CONSTRAINED OPTIMIZATION; CONVEX OPTIMIZATION; DECOMPOSITION; INTERPOLATION;

SIGNAL PROCESSING;

EID: 80052892193     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2160058     Document Type: Article

References (35)

1. E. J. Rothwell and W. Sun, "Time domain deconvolution of transient radar data," IEEE Trans. Antennas Propag., vol. 38, no. 4, pp. 470-475, Apr. 1990. (Pubitemid 20702104)
2. J. Mendel, Optimal Seismic Deconvolution: An Estimation Based Approach. New York: Academic, 1983.
3. R. D. Patterson, K. Robinson, J. Holdsworth, D. McKeown, C. Zhan, andM.Allerhand, "Complex sounds and auditory images," in Proc. 9th Int. Symp. Hearing Audit., Physiol. Perception, , 1992, pp. 429-446.
4. E. Smith andM. S.Lewicki, "Efficient coding of time-relative structure using spikes," Neural Comput., vol. 17, no. 1, pp. 19-45, Jan. 2005. (Pubitemid 40305881)
5. R. Grosse, R. Raina, H. Kwong, and A. Y. Ng, "Shift-invariant sparse coding for audio classification," in Proc. Uncertainty in Artif. Intell. (UAI), 2007, pp. 149-158.
6. E. P. Simoncelli andW. T. Freeman, "The steerable pyramid:Aflexible architecture formulti-scale derivative computation," in Proc. 2nd IEEE Int. Conf. Image Process.,Washington, DC, Oct. 23-26, 1995, vol. III, pp. 444-447.
7. S. Mallat, A Wavelet Tour of Signal Processing. NewYork:Academic, 1999.
8. P. Sallee and B. A. Olshausen, "Learning sparse multiscale image representations," in Proc. NIPS, 2002, pp. 1327-1334.
9. E. J. Candés, L. Demanet, D. L. Donoho, and L. Ying, "Fast discrete curvelet transforms," Multiscale Modeling and Simulation, vol. 5, 2005.
10. B. A. Olshausen and D. J. Field, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, no. 6583, pp. 607-609, Jun. 1996. (Pubitemid 26177476)
11. A. J. Bell and T. J. Sejnowski, "The "independent components" of natural scenes are edge filters," Vision Res., vol. 37, no. 23, pp. 3327-3338, Dec. 1997. (Pubitemid 27493806)
12. A. Hyvärinen and P. Hoyer, "Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces," Neural Comput., vol. 12, no. 7, pp. 1705-1720, Jul. 2000.
13. J. H. Friedman and J. W. Tukey, "A projection pursuit algorithm for exploratory data analysis," IEEE Trans. Comput., vol. C-23, no. 9, pp. 881-890, 1974.
14. S.Mallat and Z. Zhang, "Matching pursuitswith time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
15. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, 2004.
16. T. Blumensath and M. E. Davies, "Iterative thresholding for sparse approximations," J. Fourier Anal. Appl., vol. 14, no. 5, pp. 629-654, Dec. 2008.
17. M. Elad, "Why simple shrinkage is still relevant for redundant representations," IEEE Trans. Inf. Theory, vol. 52, pp. 5559-5569, 2006. (Pubitemid 46445399)
18. J. Bioucas-Dias and M. Figueiredo, "A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992-3004, 2007. (Pubitemid 350201232)
19. M. A. T. Figueiredo, J. M. Bioucas-Dias, and R. D. Nowak, "Majorization- minimization algorithms for wavelet-based image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, 2007. (Pubitemid 350201231)
20. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc. Series B (Methodol.), vol. 58, no. 1, pp. 267-288, 1996.
21. S. S. Chen,D. L.Donoho, andM.A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998. (Pubitemid 128689501)
22. C. Ekanadham, D. Tranchina, and E. P. Simoncelli, "Sparse decomposition of transformation-invariant signals with continuous basis pursuit," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2011.
23. G. Davis, S. Mallat, and M. Avellaneda, "Adaptive greedy approximations," Construct. Approx., vol. 13, pp. 57-98, 1997, 10.1007/BF02678430.
24. H. L. Taylor, S. C. Banks, and J. F. McCoy, "Deconvolution with the l1 norm," Geophysics, vol. 44, no. 1, p. 39, 1979.
25. M. S. O'Brien, A. N. Sinclair, and S. M. Kramer, "Recovery of a sparse spike time series by l1 normdeconvolution," IEEE Trans. Signal Process., vol. 42, no. 12, pp. 3353-3365, Dec. 1994.
26. E. J. Candés, 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, 2006. (Pubitemid 43174093)
27. I. J. Schoenberg, "On trigonometric spline interpolation," J. Math Mech., vol. 13, pp. 795-825, 1964.
28. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
29. Y. C. 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, 2009.
30. M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming, ver. 1.21 [Online]. Available: http://cvxr.com/cvx, Oct. 2010
31. "Manifold models for signals and images," Comput. Vis. Image Understand., vol. 113, no. 2, pp. 249-260, 2009.
32. P. Berkes, R. E. Turner, and M. Sahani, "A structured model of video reproduces primary visual cortical organisation," PLoS Comput. Biol., vol. 5, no. 9, Sep. 2009, e1000495.
33. M. Unser, "Sampling-50 years after Shannon," Proc. IEEE, vol. 88, no. 4, pp. 569-587, 2000.
34. M. Vetterli, P. Marziliano, and T. Blu, "Sampling signals with finite rate of innovation," IEEE Trans. Signal Process., vol. 50, no. 6, pp. 1417-1428, Jun. 2002. (Pubitemid 34822552)
35. J. Uriguen, Y. C. Eldar, P. L. Dragotti, and Z. Ben-Haim, Sampling at the Rate of Innovation: Theory and Applications. Cambridge, U.K.: Cambridge Univ. Press, 2011.