Global convergence of the Locally Competitive Algorithm

2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011 - Proceedings

Volumn , Issue , 2011, Pages 431-436

  Balavoine, Auréle ^a   Rozell, Christopher J ^a   Romberg, Justin ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

1 minimization; Compressed Sensing; continuous time; Locally Competitive Algorithm; sparse approximation

Indexed keywords

1-MINIMIZATION; COMPETITIVE ALGORITHMS; COMPRESSED SENSING; CONTINUOUS TIME; SPARSE APPROXIMATIONS;

APPROXIMATION ALGORITHMS; CONTINUOUS TIME SYSTEMS; DIGITAL SIGNAL PROCESSING; DYNAMICAL SYSTEMS; INVERSE PROBLEMS; LIFE CYCLE; OPTIMIZATION; PROBLEM SOLVING; SIGNAL PROCESSING; SIGNAL RECONSTRUCTION; SYSTEMS ANALYSIS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 79954457647     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/DSP-SPE.2011.5739253     Document Type: Conference Paper

References (20)

1. S.S. Chen, D.L. Donoho, and M.A. Saunders, "Atomic decomposition by basis pursuit," SIAM Review, vol. 43, no. 1, pp. 129-159, Mar. 2001. (Pubitemid 32406896)
2. M. Elad, "Why simple shrinkage is still relevant for redundant representations?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5559-5569, Dec. 2006. (Pubitemid 46445399)
3. E.J. Candes, 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)
4. D.L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
5. M.A.T. Figueiredo, R.D. Nowak, and S.J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 586-598, Dec. 2007.
6. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, "An Interior-Point method for Large-Scale L1-Regularized least squares," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 606-617, Dec. 2007. (Pubitemid 351266626)
7. C.J. Rozell, D.H. Johnson, R.G. Baraniuk, and B.A. Olshausen, "Sparse coding via thresholding and local competition in neural circuits," Neural Computation, vol. 20, no. 10, pp. 2526-2563, Oct. 2008.
8. C. Twigg and P. Hasler, "Configurable analog signal processing," Digital Signal Processing, vol. 19, no. 6, pp. 904-922, Dec. 2009.
9. R.A. Decarlo, M.S. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 1069-1082, July 2000.
10. H. Yang and T.S. Dillon, "Exponential stability and oscillation of hopfield graded response neural network," IEEE Trans. Neural Netw., vol. 5, no. 5, pp. 719-729, Sept. 1994, PMID: 18267846.
11. M.S. Asif and J. Romberg, "On the LASSO and dantzig selector equivalence," Conference on Information Sciences and Systems (CISS), pp. 1-6, Mar. 2010.
12. D. Donoho and Y. Tsaig, "Fast solution of l1-norm minimization problems when the solution may be sparse," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 4789-4812, Nov. 2008.
13. E.T. Hale, W. Yin, and Y. Zhang, "A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing," Tech. Rep. TR07-07, Rice University, Deparment of Computational and Applied Mathematics, July 2007.
14. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Communications on Pure and Applied Mathematics, vol. 57, no. 11, pp. 1413-1457, July 2004. (Pubitemid 39427442)
15. M.A.T. Figueiredo and R.D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
16. T. Blumensath and M.E. Davies, "Iterative thresholding for sparse approximations," Journal of Fourier Analysis and Applications, vol. 14, no. 5-6, pp. 629-654, Sept. 2008.
17. A. Bacciotti and L. Rosier, Liapunov functions and stability in control theory, Springer, 2005.
18. J. Bolte, A. Daniilidis, and A. Lewis, "The Lojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical System," SIAM Journal on Optimization, vol. 17, no. 4, pp. 1205, 2007.
19. J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1341-1344, June 2004.
20. C. Dossal, "A necessary and sufficient condition for exact recovery by l1 minimization," July 2007, Preprint Hal-00164738.