Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization

IEEE Journal on Selected Topics in Signal Processing

Volumn 10, Issue 4, 2016, Pages 782-794

  Chi, Yuejie ^a,b  

^a The Ohio State University   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

atomic norm; blind spikes deconvolution; joint spectral sparsity; lifting

Indexed keywords

CONVEX OPTIMIZATION; LINEAR SYSTEMS;

ATOMIC NORM; LIFTING; LINEAR SUPERPOSITIONS; LOW-DIMENSIONAL SUBSPACE; OPTIMIZATION FRAMEWORK; SEPARATION CONDITION; SINGLE-MOLECULE MICROSCOPY; UNDERDETERMINED LINEAR SYSTEMS;

OPTICAL TRANSFER FUNCTION;

EID: 84970966168     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2016.2543462     Document Type: Article

References (30)

1. R. Schmidt, "Multiple emitter location and signal parameter estimation, " IEEE Trans. Antennas Propag., vol. AP-34, no. 3, pp. 276-280, Mar. 1986.
2. R. Roy and T. Kailath, "ESPRIT-estimation of signal parameters via rotational invariance techniques, " IEEE Trans. Acoust. Speech Signal Process., vol. 37, no. 7, pp. 984-995, Jul. 1989.
3. E. J. Candès and C. Fernandez-Granda, "Towards a mathematical theory of super-resolution, " Commun. Pure Appl. Math., vol. 67, no. 6, pp. 906-956, 2014.
4. G. Gerstein and W. Clark, "Simultaneous studies of firing patterns in several neurons, " Science, vol. 143, no. 3612, pp. 1325-1327, 1964.
5. B. Friedlander and A. Weiss, "Eigenstructure methods for direction finding with sensor gain and phase uncertainties, " in Proc. Int. Conf. Acoust. Speech Signal Process., Apr. 1988, pp. 2681-2684.
6. Y. Li, K. Lee, and Y. Bresler, "Identifiability in blind deconvolution with subspace or sparsity constraints, " arXiv preprint arXiv:1505.03399, 2015.
7. Y. Li, K. Lee, and Y. Bresler, "A unified framework for identifiability analysis in bilinear inverse problems with applications to subspace and sparsity models, " arXiv preprint arXiv:1501.06120, 2015.
8. S. Choudhary and U. Mitra, "On identifiability in bilinear inverse problems, " in Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP), 2013, pp. 4325-4329.
9. M. Viberg and A. Swindlehurst, "A Bayesian approach to auto-calibration for parametric array signal processing, " IEEE Trans. Signal Process., vol. 42, no. 12, pp. 3495-3507, Dec. 1994.
10. A. Ahmed, B. Recht, and J. Romberg, "Blind deconvolution using convex programming, " IEEE Trans. Inf. Theory, vol. 60, no. 3, pp. 1711-1732, Mar. 2014.
11. S. Ling and T. Strohmer, "Self-calibration and biconvex compressive sensing, " Inverse Problems, vol. 31, no. 11, p. 115002, 2015.
12. K. Lee, Y. Li, M. Junge, and Y. Bresler, "Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization, " in Proc. Int. Conf. Sampling Theory Appl. (SampTA), 2015, pp. 158-162.
13. Y. Chi, "Joint sparsity recovery for spectral compressed sensing, " in Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP), 2014, pp. 3938-3942.
14. Y. Li and Y. Chi, "Off-The-grid line spectrum denoising and estimation with multiple measurement vectors, " IEEE Trans. Signal Process., vol. 64, no. 5, pp. 1257-1269, Mar. 2016.
15. E. Candès and Y. Plan, "A probabilistic and RIPless theory of compressed sensing, " IEEE Trans. Inf. Theory, vol. 57, no. 11, pp. 7235-7254, Nov. 2011.
16. G. Tang, B. N. Bhaskar, P. Shah, and B. Recht, "Compressed sensing off the grid, " IEEE Trans. Inf. Theory, vol. 59, no. 11, pp. 7465-7490, Nov. 2013.
17. Y. Chi, "Robust blind spikes deconvolution, " in Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP), 2016, pp. 2906-2910.
18. E. J. Candès, T. Strohmer, and V. Voroninski, "Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming, " Commun. Pure Appl. Math., vol. 66, no. 8, pp. 1241-1274, 2013.
19. Y. Chi, L. Scharf, A. Pezeshki, and A. Calderbank, "Sensitivity to basis mismatch in compressed sensing, " IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2182-2195, May 2011.
20. C. Fernandez-Granda, "Super-resolution of point sources via convex programming, " in Proc. IEEE 6th Int. Workshop Comput. Adv. Multi-Sensor Adaptive Process., 2015, pp. 41-44.
21. T. Bendory, S. Dekel, and A. Feuer, "Super-resolution on the sphere using convex optimization, " IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2253-2262, May 2015.
22. Y. Li and Y. Chi, "Stable separation and super-resolution of mixture models, " arXiv preprint arXiv:1506.07347, 2015.
23. V. Duval and G. Peyré, "Exact support recovery for sparse spikes deconvolution, " Found. Comput. Math., vol. 15, no. 5, pp. 1315-1355, 2015.
24. V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky, "The convex geometry of linear inverse problems, " Found. Comput. Math., vol. 12, no. 6, pp. 805-849, 2012.
25. Y. Chi and Y. Chen, "Compressive two-dimensional harmonic retrieval via atomic norm minimization, " IEEE Trans. Signal Process., vol. 63, no. 4, pp. 1030-1042, Feb. 2015.
26. M. Grant, S. Boyd, and Y. Ye. (2008). CVX: Matlab Software for Disciplined Convex Programming [Online]. Available: http://stanford.edu/~boyd/cvx
27. T. Cai and L. Wang, "Orthogonal matching pursuit for sparse signal recovery with noise, " IEEE Trans. Inf. Theory, vol. 57, no. 7, pp. 1-26, Jul. 2011.
28. S. Oymak, A. Jalali, M. Fazel, Y. C. Eldar, and B. Hassibi, "Simultaneously structured models with application to sparse and lowrank matrices, " IEEE Trans. Inf. Theory, vol. 61, no. 5, pp. 2886-2908, May 2015.
29. J. A. Tropp, "User-friendly tail bounds for sums of random matrices, " Found. Comput. Math., vol. 12, no. 4, pp. 389-434, 2012.
30. M. Talagrand, "Concentration of measure and isoperimetric inequalities in product spaces, " Publ. Math. lIHES, vol. 81, no. 1, pp. 73-205, 1995.