{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:37:38Z","timestamp":1776847058749,"version":"3.51.2"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T00:00:00Z","timestamp":1467763200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T00:00:00Z","timestamp":1467763200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-0748839"],"award-info":[{"award-number":["DMS-0748839"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS-1028790"],"award-info":[{"award-number":["ECCS-1028790"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-0926127"],"award-info":[{"award-number":["CCF-0926127"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501569"],"award-info":[{"award-number":["11501569"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61072118"],"award-info":[{"award-number":["61072118"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s10444-016-9467-y","type":"journal-article","created":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T03:43:43Z","timestamp":1467776623000},"page":"1381-1399","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations"],"prefix":"10.1007","volume":"42","author":[{"given":"Hui","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wotao","family":"Yin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,7,6]]},"reference":[{"issue":"3","key":"9467_CR1","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1088\/0266-5611\/23\/3\/007","volume":"23","author":"M Elad","year":"2007","unstructured":"Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Prob. 23(3), 947 (2007)","journal-title":"Inverse Prob."},{"issue":"6","key":"9467_CR2","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1109\/TIT.2004.828141","volume":"50","author":"JJ Fuchs","year":"2004","unstructured":"Fuchs, J.J.: On sparse representations in arbitrary redundant bases. IEEE Trans. Inf. Theory 50(6), 1341\u20131344 (2004)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"9467_CR3","doi-asserted-by":"publisher","first-page":"7235","DOI":"10.1109\/TIT.2011.2161794","volume":"57","author":"EJ Candes","year":"2011","unstructured":"Candes, E.J., Plan, Y.: A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 57(11), 7235\u20137254 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9-10","key":"9467_CR4","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.crma.2008.03.014","volume":"346","author":"E Candes","year":"2008","unstructured":"Candes, E.: The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique 346(9-10), 589\u2013592 (2008)","journal-title":"Comptes Rendus Mathematique"},{"key":"9467_CR5","doi-asserted-by":"crossref","unstructured":"Cohen, A., Dahmen, W., Devore, R.: Compressed sensing and best k-term approximation. J. Am. Math. Soc., 211\u2013231 (2009)","DOI":"10.1090\/S0894-0347-08-00610-3"},{"issue":"1","key":"9467_CR6","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s40305-013-0010-2","volume":"1","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y.: Theory of compressive sensing via \u2113\n                           1-minimization: a non-RIP analysis and extensions. J. Oper. Res. Soc. China 1(1), 79\u2013105 (2013)","journal-title":"J. Oper. Res. Soc. China"},{"issue":"7","key":"9467_CR7","doi-asserted-by":"publisher","first-page":"075014","DOI":"10.1088\/0266-5611\/27\/7\/075014","volume":"27","author":"M Grasmair","year":"2011","unstructured":"Grasmair, M: Linear convergence rates for tikhonov regularization with positively homogeneous functionals. Inverse Prob. 27(7), 075014 (2011)","journal-title":"Inverse Prob."},{"issue":"4","key":"9467_CR8","doi-asserted-by":"publisher","first-page":"2001","DOI":"10.1109\/TIT.2012.2233859","volume":"59","author":"S Vaiter","year":"2013","unstructured":"Vaiter, S., Peyre, G., Dossal, C., Fadili, J.: Robust sparse analysis regularization. IEEE Trans. Inf. Theory 59(4), 2001\u20132016 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"9467_CR9","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1109\/TSP.2012.2222396","volume":"61","author":"M Haltmeier","year":"2013","unstructured":"Haltmeier, M.: Stable signal reconstruction via \u2113\n                           1 -minimization in redundant, non-tight frames. IEEE Trans. Signal Process. 61(2), 420\u2013426 (2013)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"9467_CR10","doi-asserted-by":"publisher","first-page":"1035","DOI":"10.1137\/120868281","volume":"6","author":"D Needell","year":"2013","unstructured":"Needell, D., Ward, R.: Stable image reconstruction using total variation minimization. SIAM Journal on Imaging Sciences 6(2), 1035\u20131058 (2013)","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"10","key":"9467_CR11","doi-asserted-by":"publisher","first-page":"3941","DOI":"10.1109\/TIP.2013.2264681","volume":"22","author":"D Needell","year":"2013","unstructured":"Needell, D., Ward, R.: Near-optimal compressed sensing guarantees for total variation minimization. IEEE Trans. Image Process. 22(10), 3941\u20133949 (2013)","journal-title":"IEEE Trans. Image Process."},{"issue":"2","key":"9467_CR12","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1109\/TIP.2013.2288004","volume":"23","author":"F Krahmer","year":"2014","unstructured":"Krahmer, F., Ward, R.: Stable and robust sampling strategies for compressive imaging. IEEE Trans. Image Process. 23(2), 612\u2013622 (2014)","journal-title":"IEEE Trans. Image Process."},{"issue":"6","key":"9467_CR13","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1017\/S0956792515000236","volume":"26","author":"M Kabanava","year":"2015","unstructured":"Kabanava, M., Rauhut, H., Zhang, H.: Robust analysis \u2113\n                           1-recovery from gaussian measurements and total variation minimization. Eur. J. Appl. Math. 26(6), 917\u2013929 (2015)","journal-title":"Eur. J. Appl. Math."},{"issue":"3","key":"9467_CR14","first-page":"230","volume":"4","author":"S Vaiter","year":"2015","unstructured":"Vaiter, S., Golbabaee, M., Fadili, J., Peyr\u00e9, G.: Model selection with low complexity priors. Information and Inference 4(3), 230\u2013287 (2015)","journal-title":"Information and Inference"},{"key":"9467_CR15","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.laa.2015.09.003","volume":"486","author":"H Zhang","year":"2015","unstructured":"Zhang, H., Cheng, L.: On uniqueness guarantees of solution in convex regularized linear inverse problems. Linear Algebra Appl. 486, 475\u2013483 (2015)","journal-title":"Linear Algebra Appl."},{"issue":"5","key":"9467_CR16","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1088\/0266-5611\/20\/5\/005","volume":"20","author":"M Burger","year":"2004","unstructured":"Burger, M., Osher, S.: Convergence rates of convex variational regularization. Inverse Prob. 20(5), 1411 (2004)","journal-title":"Inverse Prob."},{"issue":"2","key":"9467_CR17","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1002\/cpa.20350","volume":"64","author":"M Grasmair","year":"2011","unstructured":"Grasmair, M., Haltmeier, M., Scherzer, O.: Necessary and sufficient conditions for linear convergence of \u2113\n                           1-regularization. Commun. Pure Appl. Math. 64(2), 161\u2013182 (2011)","journal-title":"Commun. Pure Appl. Math."},{"key":"9467_CR18","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s10957-014-0581-z","volume":"164","author":"H Zhang","year":"2015","unstructured":"Zhang, H., Yin, W., Cheng, L.: Necessary and sufficient conditions of solution uniqueness in \u2113\n                           1-norm minimization. J. Optim. Theory Appl. 164, 109\u2013122 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"9467_CR19","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s10208-013-9157-9","volume":"14","author":"M H\u00fcgel","year":"2014","unstructured":"H\u00fcgel, M., Rauhut, H., Strohme, T.: Remote sensing via \u2113\n                           1-minimization. Found. Comput. Math. 14, 115\u2013150 (2014)","journal-title":"Found. Comput. Math."},{"key":"9467_CR20","doi-asserted-by":"crossref","unstructured":"Foucart, S., Rauhut, H.: A mathematical introduction to compressive sensing. Applied and Numerical Harmonic Analysis. Birkh\u00e4user (2013)","DOI":"10.1007\/978-0-8176-4948-7"},{"issue":"1","key":"9467_CR21","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.acha.2012.03.006","volume":"34","author":"S Nam","year":"2013","unstructured":"Nam, S., Davies, M.E., Elad, M., Gribonval, R.: The cosparse analysis model and algorithms. Appl. Comput. Harmon. Anal. 34(1), 30\u201356 (2013)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9467_CR22","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259\u2013268 (1992)","journal-title":"Physica D"},{"issue":"1","key":"9467_CR23","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.acha.2010.10.002","volume":"31","author":"EJ Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s, E.J., Eldar, Y.C., Needell, D., Randall, P.: Compressed sensing with coherent and redundant dictionaries. Appl. Comput. Harmon. Anal. 31 (1), 59\u201373 (2011)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"7","key":"9467_CR24","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1109\/TIT.2012.2191612","volume":"58","author":"Y Liu","year":"2012","unstructured":"Liu, Y., Mi, T., Li, S.: Compressed sensing with general frames via optimal-dual-based \u2113\n                           1 -analysis. IEEE Trans. Inf. Theory 58(7), 4201\u20134214 (2012)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"27","key":"9467_CR25","doi-asserted-by":"publisher","first-page":"9446","DOI":"10.1073\/pnas.0502269102","volume":"102","author":"DL Donoho","year":"2005","unstructured":"Donoho, D.L., Tanner, J.: Sparse nonnegative solution of underdetermined linear equations by linear programming. Proc. Natl. Acad. Sci. U.S.A. 102(27), 9446\u20139451 (2005)","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"issue":"6","key":"9467_CR26","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1007\/s10208-012-9135-7","volume":"12","author":"V Chandrasekaran","year":"2012","unstructured":"Chandrasekaran, V., Recht, B., Parrilo, P.A., Willsky, A.S.: The convex geometry of linear inverse problems. Found. Comput. Math. 12(6), 805\u2013849 (2012)","journal-title":"Found. Comput. Math."},{"issue":"1","key":"9467_CR27","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s10440-014-9984-y","volume":"140","author":"M Kabanava","year":"2015","unstructured":"Kabanava, M., Rauhut, H.: Analysis \u2113\n                           1-recovery with frames and gaussian measurements. Acta Applicandae Mathematicae 140(1), 173\u2013195 (2015)","journal-title":"Acta Applicandae Mathematicae"},{"key":"9467_CR28","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.laa.2012.10.003","volume":"441","author":"S Foucart","year":"2014","unstructured":"Foucart, S.: Stability and robustness of \u2113\n                           1-minimizations with weibull matrices and redundant dictionaries. Linear Algebra Appl. 441, 4\u201321 (2014)","journal-title":"Linear Algebra Appl."},{"issue":"10","key":"9467_CR29","doi-asserted-by":"publisher","first-page":"3601","DOI":"10.1109\/TIT.2005.855614","volume":"51","author":"JJ Fuchs","year":"2005","unstructured":"Fuchs, J.J.: Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inf. Theory 51(10), 3601\u20133608 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9467_CR30","doi-asserted-by":"publisher","first-page":"1456","DOI":"10.1214\/13-EJS815","volume":"7","author":"RJ Tibshirani","year":"2013","unstructured":"Tibshirani, R.J.: The lasso problem and uniqueness. Electronic Journal of Statistics 7, 1456\u20131490 (2013)","journal-title":"Electronic Journal of Statistics"},{"key":"9467_CR31","unstructured":"Fadili, J., Peyr\u00e9, G., Vaiter, S., Deledalle, C.-A., Salmon, J.: Stable Recovery with Analysis Decomposable Priors. In: Proceedings of Signal Processing with Adaptive Sparse Structured Representations (SPARS) (2013)"},{"issue":"10","key":"9467_CR32","doi-asserted-by":"publisher","first-page":"2231","DOI":"10.1109\/TIT.2004.834793","volume":"50","author":"JA Tropp","year":"2004","unstructured":"Tropp, J.A.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231\u20132242 (2004)","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9467-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-016-9467-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9467-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T15:35:28Z","timestamp":1589729728000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-016-9467-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,6]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["9467"],"URL":"https:\/\/doi.org\/10.1007\/s10444-016-9467-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,6]]},"assertion":[{"value":"30 October 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 June 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}