×
Nigam, H. K.; Yadav, Saroj

Block-sparse recovery and rank minimization using a weighted \(l_p-l_q\) model. (English) Zbl 1532.90086

J. Inequal. Appl. 2023, Paper No. 29, 17 p. (2023).

MSC:

90C26 Nonconvex programming, global optimization
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
15A83 Matrix completion problems

Keywords:

nonconvexity; compressed sensing; block-RIP; matrix-RIP; block-sparse recovery; rank minimization

Software:

PDCO
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Donoho, D. L., Compressed sensing, IEEE Trans. Inf. Theory, 52, 1289-1306 (2006) · Zbl 1288.94016 · doi:10.1109/TIT.2006.871582
[2] Candès, E. J.; Romberg, J.; Tao, T., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, 52, 489-509 (2006) · Zbl 1231.94017 · doi:10.1109/TIT.2005.862083
[3] Candès, E. J.; Romberg, J.; Tao, T., Stable signal recovery from incomplete and inaccurate measurements, Commun. Pure Appl. Math., 59, 1207-1223 (2006) · Zbl 1098.94009 · doi:10.1002/cpa.20124
[4] Candès, E. J., The restricted isometry property and its implications for compressed sensing, C. R. Acad. Sci., Sér., 346, 589-592 (2008) · Zbl 1153.94002
[5] Chen, S.; Donoho, D.; Saunders, M. A., Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20, 33-61 (1998) · Zbl 0919.94002 · doi:10.1137/S1064827596304010
[6] Natarajan, B. K., Sparse approximate solutions to linear systems, SIAM J. Sci. Comput., 24, 227-234 (1995) · Zbl 0827.68054 · doi:10.1137/S0097539792240406
[7] Gribnoval, R.; Nielsen, M., Sparse representations in unions of bases, IEEE Trans. Inf. Theory, 49, 3320-3325 (2003) · Zbl 1286.94032 · doi:10.1109/TIT.2003.820031
[8] Majumdar, A.; Ward, R., Compressed sensing of color images, Signal Process., 90, 12, 3122-3127 (2010) · Zbl 1197.94089 · doi:10.1016/j.sigpro.2010.05.016
[9] Malioutov, D.; Cetin, M.; Willsky, A., Sparse signal reconstruction perspective for source localization with sensor arrays, IEEE Trans. Signal Process., 53, 8, 3010-3022 (2005) · Zbl 1370.94191 · doi:10.1109/TSP.2005.850882
[10] Parvaresh, F.; Vikalo, H.; Misra, S.; Hassibi, B., Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays, IEEE J. Sel. Top. Signal Process., 2, 3, 275-285 (2008) · doi:10.1109/JSTSP.2008.924384
[11] Mishali, M.; Eldar, Y. C., Reduce and boost: recovering arbitrary sets of jointly sparse vectors, IEEE Trans. Signal Process., 56, 10, 4692-4702 (2008) · Zbl 1390.94306 · doi:10.1109/TSP.2008.927802
[12] Vidal, R.; Ma, Y., A unified algebraic approach to 2-D and 3-D motion segmentation and estimation, J. Math. Imaging Vis., 25, 3, 403-421 (2005) · Zbl 1478.68411 · doi:10.1007/s10851-006-8286-z
[13] Erickson, S.; Sabatti, C., Empirical Bayes estimation of a sparse vector of gene expression changes, Stat. Appl. Genet. Mol. Biol., 4 (2005) · Zbl 1081.62093 · doi:10.2202/1544-6115.1132
[14] Cotter, S.; Rao, B., Sparse channel estimation via matching pursuit with application to equalization, IEEE Trans. Commun., 50, 3, 374-377 (2002) · doi:10.1109/26.990897
[15] Huang, S.; Yang, Y.; Yang, D., Class specific sparse representation for classification, Signal Process., 116, 38-42 (2015) · doi:10.1016/j.sigpro.2015.04.018
[16] Liu, Y.; Wan, Q., Enhanced compressive wideband frequency spectrum sensing for dynamic spectrum access, EURASIP J. Adv. Signal Process., 2012, 177, 1-11 (2012)
[17] Chen, W.; Li, Y., The high order RIP condition for signal recovery, J. Comput. Math., 37, 1, 61-75 (2019) · Zbl 1438.94033 · doi:10.4208/jcm.1710-m2017-0175
[18] Gao, Y.; Ma, M., A new bound on the block restricted isometry constant in compressed sensing, J. Inequal. Appl., 2017 (2017) · Zbl 1380.46008 · doi:10.1186/s13660-017-1448-2
[19] Wang, Y.; Wang, J.; Xu, Z., Restricted p-isometry properties of nonconvex blocksparse compressed sensing, Signal Process., 104, 188-196 (2014) · doi:10.1016/j.sigpro.2014.03.040
[20] Cai, Y.: Weighted \(l_p-l_1\) minimization methods for block sparse recovery and rank minimization. Anal. Appl. (2020)
[21] Wen, J.; Zhou, Z.; Liu, Z.; Lai, M.; Tang, X., Sharp sufficient conditions for stable recovery of block sparse signals by block orthogonal matching pursuit, Appl. Comput. Harmon. Anal., 47, 3, 948-974 (2019) · Zbl 1422.94017 · doi:10.1016/j.acha.2018.02.002
[22] Lin, L.; Li, S., Block sparse recovery via mixed l2/l1 minimization, Acta Math. Sin., 29, 7, 1401-1412 (2013) · Zbl 1322.94034 · doi:10.1007/s10114-013-1564-y
[23] Candès, E. J.; Tao, T., Decoding by linear programming, IEEE Trans. Inf. Theory, 51, 12, 4203-4215 (2005) · Zbl 1264.94121 · doi:10.1109/TIT.2005.858979
[24] Eldar, Y.; Mishali, M., Robust recovery of signals from a structured union of subspaces, IEEE Trans. Inf. Theory, 55, 11, 5302-5316 (2009) · Zbl 1367.94087 · doi:10.1109/TIT.2009.2030471
[25] Tomasi, C.; Kanade, T., Shape and motion from image streams under orthography: a factorization method, Int. J. Comput. Vis., 9, 1, 137-154 (1992) · doi:10.1007/BF00129684
[26] Basri, R.; Jacobs, D., Lambertian reflectance and linear subspaces, IEEE Trans. Pattern Anal. Mach. Intell., 25, 2, 218-233 (2003) · doi:10.1109/TPAMI.2003.1177153
[27] Abernethy, J.; Bach, F.; Evgeniou, T.; Vert, J. P., A new approach to collaborative filtering: operator estimation with spectral regularization, J. Mach. Learn. Res., 10, 803-826 (2009) · Zbl 1235.68122
[28] Rennie, J. D.M.; Srebro, N., Fast maximum margin matrix factorization for collaborative prediction, Proc. Int. Conf. Mach. Learn., 713-719 (2005)
[29] Mesbahi, M.; Papavassilopoulos, G. P., On the rank minimization problem over a positive semidefinite linear matrix inequality, IEEE Trans. Autom. Control, 42, 2, 239-243 (1997) · Zbl 0872.93029 · doi:10.1109/9.554402
[30] Srebro, N.: Learning with matrix factorizations. Ph.D. dissertation, Massachusetts Inst. Technol, Cambridge, MA, USA (2004)
[31] Gross, D.; Liu, Y. K.; Flammia, S. T.; Becker, S.; Eisert, J., Quantum state tomography via compressed sensing, Phys. Rev. Lett., 105 (2010) · doi:10.1103/PhysRevLett.105.150401
[32] Liu, Z.; Vandenberghe, L., Interior-point method for nuclear norm approximation with application to system identification, SIAM J. Matrix Anal. Appl., 31, 3, 1235-1256 (2009) · Zbl 1201.90151 · doi:10.1137/090755436
[33] Amit, Y., Fink, M., Srebro, N., Ullman, S.: Uncovering shared structures in multiclass classification. In: Proc. 24th Int. Conf. Mach. Learn., pp. 17-24. (2007)
[34] Morita, T.; Kanade, T., A sequential factorization method for recovering shape and motion from image streams, IEEE Trans. Pattern Anal. Mach. Intell., 19, 8, 858-867 (1997) · doi:10.1109/34.608289
[35] Zhang, M.; Huang, Z. H.; Zhang, Y., Restricted p-isometry properties of nonconvex matrix recovery, IEEE Trans. Inf. Theory, 59, 7, 4316-4323 (2013) · Zbl 1364.94179 · doi:10.1109/TIT.2013.2250577
[36] Ma, T. H.; Lou, Y.; Huang, T. Z., Truncated \(l_{1-2}\) models for sparse recovery and rank minimization, SIAM J. Imaging Sci., 10, 3, 1346-1380 (2017) · Zbl 1397.94021 · doi:10.1137/16M1098929
[37] Candès, E. J.; Tao, T., The power of convex relaxation: near-optimal matrix completion, IEEE Trans. Inf. Theory, 56, 5, 2053-2080 (2010) · Zbl 1366.15021 · doi:10.1109/TIT.2010.2044061
[38] Fazel, M.; Hindi, H.; Boyd, S., A rank minimization heuristic with application to minimum order system approximation, Proc. IEEE Amer. Control Conf, 4734-4739 (2001)
[39] Candès, E. J.; Plan, Y., Tight oracle bounds for low-rank recovery from a minimal number of random measurements, IEEE Trans. Inf. Theory, 57, 4, 2342-2359 (2011) · Zbl 1366.90160 · doi:10.1109/TIT.2011.2111771
[40] Kong, L.C., Xiu, N.H.: Exact low-rank matrix recovery via non-convex \(M_p\)-minimization, Optimization. - Online (2011)
[41] Recht, B.; Fazel, M.; Parrilo, P. A., Guaranteed minimum rank solutions of linear matrix equations via nuclear norm minimization, SIAM Rev., 52, 2, 471-501 (2010) · Zbl 1198.90321 · doi:10.1137/070697835
[42] Esser, E.; Lou, Y.; Xin, J., A method for finding structured sparse solutions to nonnegative least squares problems with applications, SIAM J. Imaging Sci., 6, 2010-2046 (2013) · Zbl 1282.90239 · doi:10.1137/13090540X
[43] Yin, P.; Lou, Y.; He, Q.; Xin, J., Minimization of \(l_{1-2}\) for compressed sensing, SIAM J. Sci. Comput., 37, 536-563 (2015) · Zbl 1316.90037 · doi:10.1137/140952363
[44] Wang, D.; Zhang, Z., Generalized sparse recovery model and its neural dynamical optimization method for compressed sensing, Circuits Syst. Signal Process., 36, 4326-4353 (2017) · Zbl 1373.94725 · doi:10.1007/s00034-017-0532-7
[45] Zhao, Y.; He, X.; Huang, T.; Huang, J., Smoothing inertial projection neural network for minimization \(L_{p-q}\) in sparse signal reconstruction, Neural Netw., 99, 33-41 (2018) · Zbl 1456.94024 · doi:10.1016/j.neunet.2017.12.008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.