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Zhang, \u201cCompressed sensing and affine rank minimization under restricted isometry,\u201d IEEE Trans. Signal Process., vol.61, no.7, pp.3279-3290, 2013. 10.1109\/tsp.2013.2259164","DOI":"10.1109\/TSP.2013.2259164"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] T. Cai and A. Zhang, \u201cSparse representation of a polytope and recovery of sparse signals and low-rank matrices,\u201d IEEE Trans. Inf. Theory, vol.60, no.1, pp.122-132, 2014. 10.1109\/tit.2013.2288639","DOI":"10.1109\/TIT.2013.2288639"},{"key":"3","doi-asserted-by":"crossref","unstructured":"[3] D. Donoho and X. Huo, \u201cUncertainty principles and ideal atomic decomposition,\u201d IEEE Trans. Inf. Theory, vol.47, no.7, pp.2845-2862, 2001. 10.1109\/18.959265","DOI":"10.1109\/18.959265"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] E. Candes and T. Tao, \u201cNear-optimal signal recovery from random projections: Universal encoding strategies?,\u201d IEEE Trans. Inf. Theory, vol.52, no.12, pp.5406-5425, 2006. 10.1109\/tit.2006.885507","DOI":"10.1109\/TIT.2006.885507"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] D. Donoho, \u201cCompressed sensing,\u201d IEEE Trans. Inf. Theory, vol.52, no.4, pp.1289-1306, 2006. 10.1109\/tit.2006.871582","DOI":"10.1109\/TIT.2006.871582"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] J. Romberg, \u201cImaging via compressive sampling,\u201d IEEE Signal Process. Mag., vol.25, no.2, pp.14-20, 2008. 10.1109\/msp.2007.914729","DOI":"10.1109\/MSP.2007.914729"},{"key":"7","unstructured":"[7] S. Bahmani and J. Romberg, \u201cEfficient compressive phase retrieval with constrained sensing vectors,\u201d NIPS, 2015."},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] E. Candes and T. Tao, \u201cThe Dantzig selector: Statistical estimation when <i>p<\/i> is much larger than <i>n<\/i>,\u201d Ann. Statist., vol.35, no.6, pp.2313-2351, 2007. 10.1214\/009053606000001523","DOI":"10.1214\/009053606000001523"},{"key":"9","unstructured":"[9] K. Gregor and Y. LeCun, \u201cLearning fast approximations of sparse coding,\u201d ICML, 2010."},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] M.A. Davenport, P.T. Boufounos, M.B. Wakin, and R.G. Baraniuk, \u201cSignal processing with compressive measurements,\u201d IEEE J. Sel. Topics Signal Process., vol.4, no.2, pp.445-460, 2010. 10.1109\/jstsp.2009.2039178","DOI":"10.1109\/JSTSP.2009.2039178"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] M. Davenport, J. Laska, J. Treichler, and R. Baraniuk, \u201cThe pros and cons of compressive sensing for wideband signal acquisition: Noise folding versus dynamic range,\u201d IEEE Trans. Signal Process., vol.60, no.9, pp.4628-4642, 2012. 10.1109\/tsp.2012.2201149","DOI":"10.1109\/TSP.2012.2201149"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] S.K. Sharma, E. Lagunas, S. Chatzinotas, and B. Ottersten, \u201cApplication of compressive sensing in cognitive radio communications: A survey,\u201d IEEE Commun. Surveys Tuts., vol.18, no.3, pp.1838-1860, 2016. 10.1109\/comst.2016.2524443","DOI":"10.1109\/COMST.2016.2524443"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[13] J. Li, H. Liu, and Y. Fu, \u201cPredictive coding machine for compressed sensing and image denoising,\u201d Proc. AAAI Conf. on Artif. Intell., pp.3506-3513, 2018.","DOI":"10.1609\/aaai.v32i1.11626"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] E. Candes and T. Tao, \u201cDecoding by linear programming,\u201d IEEE Trans. Inf. Theory, vol.51, no.12, pp.4203-4215, 2005. 10.1109\/tit.2005.858979","DOI":"10.1109\/TIT.2005.858979"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] B. Olshausen and D. Field, \u201cSparse coding with an overcomplete basis set: A strategy employed by V1?,\u201d Vision Research, vol.37, no.23, pp.3311-3325, 1997. 10.1016\/s0042-6989(97)00169-7","DOI":"10.1016\/S0042-6989(97)00169-7"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] E. Candes and T. Tao, \u201cThe Dantzig selector: Statistical estimation when is much larger than <i>n<\/i>,\u201d Ann. Statist., vol.35, no.6, pp.2313-2351, 2007. 10.1214\/009053606000001523","DOI":"10.1214\/009053606000001523"},{"key":"17","doi-asserted-by":"crossref","unstructured":"[17] A. Bruckstein, D. Donoho, and M. Elad, \u201cFrom sparse solutions of systems of equations to sparse modeling of signals and images,\u201d SIAM Review, vol.51, no.1, pp.34-81, 2009. 10.1137\/060657704","DOI":"10.1137\/060657704"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] A. Tillmann and M. 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Wang, and G. Xu, \u201cShifting inequality and recovery of sparse signals,\u201d IEEE Trans. Signal Process., vol.58, no.3, pp.1300-1308, 2010. 10.1109\/tsp.2009.2034936","DOI":"10.1109\/TSP.2009.2034936"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] T. Cai and A. Zhang, \u201cSharp RIP bound for sparse signal and low-rank matrix recovery,\u201d Applied and Computational Harmonic Analysis, vol.35, no.1, pp.74-93, 2013. 10.1016\/j.acha.2012.07.010","DOI":"10.1016\/j.acha.2012.07.010"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] S. Dirksen, G. Lecue, and H. Rauhut, \u201cOn the gap between restricted isometry properties and sparse recovery conditions,\u201d IEEE Trans. Inf. Theory, vol.64, no.8, pp.5478-5487, 2018. 10.1109\/tit.2016.2570244","DOI":"10.1109\/TIT.2016.2570244"},{"key":"24","doi-asserted-by":"publisher","unstructured":"[24] J. Cahill, X. Chen, and R. 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Nielsen, \u201cSparse representations in unions of bases,\u201d IEEE Trans. Inf. Theory, vol.49, no.12, pp.3320-3325, 2003. 10.1109\/tit.2003.820031","DOI":"10.1109\/TIT.2003.820031"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[28] L.G.A. d&apos;Aspremont, \u201cTesting the nullspace property using semidefinite programming,\u201d Math. Program., Series B, vol.127, no.1, pp.123-144, 2011. 10.1007\/s10107-010-0416-0","DOI":"10.1007\/s10107-010-0416-0"},{"key":"29","doi-asserted-by":"publisher","unstructured":"[29] Q. Sun, \u201cSparse approximation property and stable recovery of sparse signals from noisy measurements,\u201d IEEE Trans. Signal Process., vol.59, no.10, pp.5086-5090, 2011. 10.1109\/tsp.2011.2161470","DOI":"10.1109\/TSP.2011.2161470"},{"key":"30","doi-asserted-by":"crossref","unstructured":"[30] M. Cho and W. 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DeVore, \u201cCompressed sensing and best <i>k<\/i>-term approximation,\u201d J. Am. Math. Soc., vol.22, no.1, pp.211-231, 2009. 10.1090\/s0894-0347-08-00610-3","DOI":"10.1090\/S0894-0347-08-00610-3"},{"key":"34","unstructured":"[34] M. Davies and R. Gribonval, \u201cOn Lp minimisation, instance optimality, and restricted isometry constants for sparse approximation,\u201d Proc. Sampling Theory and Applications (SampTA), 2009."},{"key":"35","doi-asserted-by":"crossref","unstructured":"[35] M. Stojnic, W. Xu, and B. Hassibi, \u201cCompressed sensing-probabilistic analysis of a null-space characterization,\u201d IEEE Internat. Conf. on Acoustics, Speech and Signal Processing, ICASSP, 2008. 10.1109\/icassp.2008.4518375","DOI":"10.1109\/ICASSP.2008.4518375"},{"key":"36","unstructured":"[36] D. Ba, B. Babadi, P. Purdon, and E. 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Signal Process., vol.62, no.19, pp.4984-4996, 2014. 10.1109\/tsp.2014.2343949","DOI":"10.1109\/TSP.2014.2343949"},{"key":"40","doi-asserted-by":"publisher","unstructured":"[40] R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, \u201cA simple proof of the restricted isometry property for random matrices,\u201d Constr. 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