Donoho, David L. Compressed sensing. (English) Zbl 1288.94016 IEEE Trans. Inf. Theory 52, No. 4, 1289-1306 (2006). Cited in 4 ReviewsCited in 1270 Documents MSC: 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 68U10 Computing methodologies for image processing Keywords:Integrated sensing and processing; optimal recovery; information-based complexity; Gelfand n-widths; adaptive sampling; sparse solution of linear equations; Basis Pursuit; minimum \(\ell^1\) norm decomposition; almost-spherical sections of Banach spaces PDF BibTeX XML Cite \textit{D. L. Donoho}, IEEE Trans. Inf. Theory 52, No. 4, 1289--1306 (2006; Zbl 1288.94016) Full Text: DOI OpenURL References: [1] Donoho D L. Compressed sensing. IEEE Trans Inf Theory, 2006, 52: 1289-1306 · Zbl 1288.94016 [2] Candes E J, Tao T. Decoding by linear programming. IEEE Trans Inf Theory, 2005, 51:4203-4215 · Zbl 1264.94121 [3] Candes E J, Romberg J, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math, 2006, 59: 1207-1223 · Zbl 1098.94009 [4] Candes E J. The restricted isometry property and its implications for compressed sensing. C R Math, 2008, 346: 589-592 · Zbl 1153.94002 [5] Foucart S, Lai M. Sparsest solutions of underdetermined linear systems via \(l_q\)-minimization for \(0 < q < 1\). Appl Comput Harmon Anal, 2009, 2613: 395-407 · Zbl 1171.90014 [6] Cai T, Wang L, Xu G. Shift inequality and recovery of sparse signals. IEEE Trans Signal Process, 2010, 58: 1300-1308 · Zbl 1392.94117 [7] Cai T, Wang L, Xu G. New bounds for restricted isometry constants. IEEE Trans Inf Theory, 2010, 56: 4388-4394 · Zbl 1366.94181 [8] Fang Y, Wu J J, Huang B M. 2D sparse signal recovery via 2D orthogonal matching pursuit. Sci China Inf Sci, 2012, 55: 889-897 · Zbl 1245.94034 [9] Zhang H, Liang Y, Gou H L, et al. The essential ability of sparse reconstruction of different compressive sensing strategies. Sci China Inf Sci, 2012, 55: 2582-2589 · Zbl 1270.94046 [10] Zhang B C, Hong W, Wu Y R. Sparse microwave imaging: Principles and applications. Sci China Inf Sci, 2012, 55: 1722-1754 · Zbl 1270.94026 [11] Liu H P, Sun F C. Fusion tracking in color and infrared images using joint sparse representation. Sci China Inf Sci, 2012, 55: 590-599 [12] Candes E J, Tao T. The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). Ann Statist, 2007, 35: 2313-2351 · Zbl 1139.62019 [13] Cai T, Xu G, Zhang J. On recovery of sparse signals via \(l_1\) minimization. IEEE Trans Inf Theory, 2009, 55: 3388-3397 · Zbl 1367.94081 [14] Davies M E, 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.