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We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm.
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A. S. Bandeira, M. Fickus, D. G. Mixon, P. Wong, The road to deterministic matrices with the restricted isometry property, J. Fourier Anal. Appl. 19 (2013) 1123–1149
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R. Gribonval, M. Nielsen, Highly sparse representations from dictionaries are unique and independent of the sparseness measure, Appl. Comput. Harmon. Anal. 22 (2007) 335–355
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O. Guédon, S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Majorizing measures and proportional subsets of bounded orthonormal systems, Rev. Mat. Iberoam. 24 (2008) 1075–1095
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M. Rudelson, R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements, Comm. Pure Appl. Math. 61 (2008) 1025–1045
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J. A. Tropp, On the linear independence of spikes and sines, J. Fourier Anal. Appl. 14 (2008) 838–858
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T. T. Cai, A. Zhang, Sharp RIP bound for sparse signal and low-rank matrix recovery, Appl. Comput. Harmon. Anal. 35 (2013) 74–93
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A. Foucart, H. Rauhut, A Mathematical Introduction to Compressive Sensing, Applied and Numerical Harmonic Analysis, Birkhäuser, 2013
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M. E. Lopes, Estimating unknown sparsity in compressed sensing, JMLR W&CP 28 (2013) 217–225
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J. Bourgain, An improved estimate in the restricted isometry problem, Lect. Notes Math. 2116 (2014) 65–70
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P. Indyk, M. Kapralov, Sample-optimal Fourier sampling in any constant dimension, FOCS 2014, 514–523
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M. B. McCoy, V. Cevher, Q. T. Dinh, A. Asaei, L. Baldassarre, Convexity in source separation: Models, geometry, and algorithms, Signal Proc. Mag. 31 (2014) 87–95
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M. B. McCoy, J. A. Tropp, Sharp recovery bounds for convex demixing, with applications, Found. Comput. Math. 14 (2014) 503–567
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J. Nelson, E. Price, M. Wootters, New constructions of RIP matrices with fast multiplication and fewer rows, SODA 2014, 1515–1528
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A. Repetti, M. Q. Pham, L. Duval, É. Chouzenoux, J.-C. Pesquet, Euclid in a taxicab: Sparse blind deconvolution with smoothed ℓ 1 / ℓ 2 \ell_{1}/\ell_{2} regularization, IEEE Signal Process. Lett. 22 (2014) 539–543
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