{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:07:17Z","timestamp":1776845237229,"version":"3.51.2"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,4,23]],"date-time":"2009-04-23T00:00:00Z","timestamp":1240444800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2010,2]]},"DOI":"10.1007\/s10208-009-9046-4","type":"journal-article","created":{"date-parts":[[2009,4,22]],"date-time":"2009-04-22T02:23:16Z","timestamp":1240366996000},"page":"1-13","source":"Crossref","is-referenced-by-count":68,"title":["Stability and Instance Optimality for Gaussian Measurements in Compressed Sensing"],"prefix":"10.1007","volume":"10","author":[{"given":"P.","family":"Wojtaszczyk","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,4,23]]},"reference":[{"issue":"3","key":"9046_CR1","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s00365-007-9003-x","volume":"28","author":"R. Baraniuk","year":"2008","unstructured":"R. Baraniuk, M. Davenport, R. DeVore, M. Wakin, A simple proof of the restricted isometry property for random matrices, Constr. Approx. 28(3), 253\u2013263 (2008).","journal-title":"Constr. Approx."},{"key":"9046_CR2","unstructured":"E. Candes, Compressive sampling, in Proc. Intl. Congress Math., Madrid, 2006."},{"key":"9046_CR3","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.crma.2008.03.014","volume":"346","author":"E. Candes","year":"2008","unstructured":"E. Candes, The restricted isometry property and its implications for compressed sensing, C. R. Acad. Sci. Paris, Ser. I 346, 589\u2013592 (2008).","journal-title":"C. R. Acad. Sci. Paris, Ser. I"},{"key":"9046_CR4","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"E. Candes","year":"2006","unstructured":"E. Candes, J. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Commun. Pure Appl. Math. 59, 1207\u20131223 (2006).","journal-title":"Commun. Pure Appl. Math."},{"key":"9046_CR5","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E. Candes","year":"2004","unstructured":"E. Candes, T. Tao, Near optimal recovery from random projections: universal encoding strategies, IEEE Trans. Inf. Theory 52, 5406\u20135425 (2004).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9046_CR6","doi-asserted-by":"crossref","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"E. Candes","year":"2005","unstructured":"E. Candes, T. Tao, Decoding by linear programing, IEEE Trans. Inf. Theory 51, 4203\u20134215 (2005).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"9046_CR7","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1090\/S0894-0347-08-00610-3","volume":"22","author":"A. Cohen","year":"2009","unstructured":"A. Cohen, W. Dahmen, R. DeVore, Compressed sensing and best k-term approximation, J. Am. Math. Soc. 22(1), 211\u2013231 (2009).","journal-title":"J. Am. Math. Soc."},{"key":"9046_CR8","unstructured":"R. DeVore, G. Petrova, P. Wojtaszczyk, Instance-optimality in probability with an \u2113 1-minimization decoder. http:\/\/www.dsp.ece.rice.edu\/cs\/ ."},{"key":"9046_CR9","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"D. Donoho","year":"2006","unstructured":"D. Donoho, Compressed sensing, IEEE Trans. Inf. Theory 52, 1289\u20131306 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9046_CR10","first-page":"1048","volume":"277","author":"A. Garnaev","year":"1984","unstructured":"A. Garnaev, E.D. Gluskin, The widths of Euclidean balls, Dokl. Akad. Nauk SSSR 277, 1048\u20131052 (1984).","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"9046_CR11","first-page":"334","volume":"41","author":"B.S. Kashin","year":"1977","unstructured":"B.S. Kashin, The widths of certain finite dimensional sets and classes of smooth functions, Izv. Akad. Nauk SSSR 41, 334\u2013351 (1977).","journal-title":"Izv. Akad. Nauk SSSR"},{"issue":"4","key":"9046_CR12","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/S1631-073X(02)02476-7","volume":"335","author":"A. Litvak","year":"2002","unstructured":"A. Litvak, P. Mankiewicz, N. Tomczak-Jaegermann, Randomized isomorphic Dvoretzky theorem, C.\u00a0R. Math. Acad. Sci. Paris 335(4), 345\u2013350 (2002).","journal-title":"C.\u00a0R. Math. Acad. Sci. Paris"},{"key":"9046_CR13","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.aim.2004.08.004","volume":"195","author":"A. Litvak","year":"2005","unstructured":"A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195, 491\u2013523 (2005).","journal-title":"Adv. Math."},{"key":"9046_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-60932-9","volume-title":"Constructive Approximation; Advanced Problems","author":"G.G. Lorentz","year":"1996","unstructured":"G.G. Lorentz, M.V. Golitschek, Y. Makovoz, Constructive Approximation; Advanced Problems (Springer, Berlin, 1996)."},{"issue":"5","key":"9046_CR15","doi-asserted-by":"crossref","first-page":"999","DOI":"10.4153\/CJM-2000-042-8","volume":"52","author":"P. Mankiewicz","year":"2000","unstructured":"P. Mankiewicz, Compact groups of operators on subproportional quotients of \u2113 1 m , Canad. J. Math. 52(5), 999\u20131017 (2000).","journal-title":"Canad. J. Math."},{"key":"9046_CR16","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.crma.2005.04.032","volume":"340","author":"S. Mendelson","year":"2005","unstructured":"S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Reconstruction and subgaussian processes, C. R. Acad. Sci. Paris, Ser. I Math. 340, 885\u2013888 (2005).","journal-title":"C. R. Acad. Sci. Paris, Ser. I Math."},{"issue":"3","key":"9046_CR17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s00365-007-9005-8","volume":"28","author":"S. Mendelson","year":"2008","unstructured":"S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Uniform uncertainity principle for Bernoulli and subgaussian ensembles, Constr. Approx. 28(3), 277\u2013289 (2008).","journal-title":"Constr. Approx."},{"key":"9046_CR18","unstructured":"D. Needell, R. Vershynin, Uniform uncertainty principle and signal recovery via regularised orthogonal matching pursuit. http:\/\/www.dsp.ece.rice.edu\/cs\/ ."},{"key":"9046_CR19","unstructured":"D. Needell, R. Vershynin, Signal recovery from incomplete and inaccurate measurements via regularised orthogonal matching pursuit. http:\/\/www.dsp.ece.rice.edu\/cs\/ ."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-009-9046-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-009-9046-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-009-9046-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T11:05:10Z","timestamp":1559127910000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-009-9046-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,23]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,2]]}},"alternative-id":["9046"],"URL":"https:\/\/doi.org\/10.1007\/s10208-009-9046-4","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4,23]]}}}