{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T05:52:05Z","timestamp":1725861125418},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319422930"},{"type":"electronic","value":"9783319422947"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-42294-7_19","type":"book-chapter","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T15:00:47Z","timestamp":1468249247000},"page":"222-231","source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Guarantees of Total Variation Minimization"],"prefix":"10.1007","author":[{"given":"Hao","family":"Jiang","sequence":"first","affiliation":[]},{"given":"Tao","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Pei-Bing","family":"Du","sequence":"additional","affiliation":[]},{"given":"Sheng-Guo","family":"Li","sequence":"additional","affiliation":[]},{"given":"Chun-Jiang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Li-Zhi","family":"Cheng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,12]]},"reference":[{"key":"19_CR1","unstructured":"Tropp, J.A.: Convex recovery of a structured signal from independent random linear measurements (2014). arXiv:1405.1102"},{"issue":"3","key":"19_CR2","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1093\/imaiai\/iau005","volume":"3","author":"D Amelunxen","year":"2014","unstructured":"Amelunxen, D., Lotz, M., McCoy, M.B., et al.: Living on the edge: phase transitions in convex programs with random data. Inform. Inf. 3(3), 224\u2013294 (2014). iau005","journal-title":"Inform. Inf."},{"issue":"3","key":"19_CR3","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s10208-014-9191-2","volume":"14","author":"MB McCoy","year":"2014","unstructured":"McCoy, M.B., Tropp, J.A.: Sharp recovery bounds for convex demixing, with applications. Found. Comput. Math. 14(3), 503\u2013567 (2014)","journal-title":"Found. Comput. Math."},{"issue":"2","key":"19_CR4","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s10208-014-9221-0","volume":"15","author":"G Lerman","year":"2015","unstructured":"Lerman, G., McCoy, M.B., Tropp, J.A., et al.: Robust computation of linear models by convex relaxation. Found. Comput. Math. 15(2), 363\u2013410 (2015)","journal-title":"Found. Comput. Math."},{"issue":"2","key":"19_CR5","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1109\/TIT.2013.2293654","volume":"60","author":"R Foygel","year":"2014","unstructured":"Foygel, R., Mackey, L.: Corrupted sensing: novel guarantees for separating structured signals. IEEE Trans. Inform. Theory 60(2), 1223\u20131247 (2014)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"19_CR6","unstructured":"Vershynin, R.: Estimation in high dimensions: a geometric perspective (2014). arXiv:1405.5103"},{"issue":"1","key":"19_CR7","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259\u2013268 (1992)","journal-title":"Physica D"},{"key":"19_CR8","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1090\/S0894-0347-2012-00740-1","volume":"25","author":"JF Cai","year":"2012","unstructured":"Cai, J.F., Dong, B., Osher, S., et al.: Image restoration: total variation, wavelet frames, and beyond. J. Am. Math. Soc. 25, 1033\u20131089 (2012)","journal-title":"J. Am. Math. Soc."},{"issue":"3","key":"19_CR9","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1137\/080724265","volume":"1","author":"Y Wang","year":"2008","unstructured":"Wang, Y., Yang, J., Yin, W., et al.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1(3), 248\u2013272 (2008)","journal-title":"SIAM J. Imag. Sci."},{"issue":"4","key":"19_CR10","first-page":"328","volume":"4","author":"JF Cai","year":"2015","unstructured":"Cai, J.F., Xu, W.: Guarantees of total variation minimization for signal recovery. Inform. Inf. 4(4), 328\u2013353 (2015)","journal-title":"Inform. Inf."},{"issue":"1","key":"19_CR11","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1109\/TIT.2012.2207945","volume":"59","author":"Y Plan","year":"2013","unstructured":"Plan, Y., Vershynin, R.: Robust 1-bit compressed sensing and sparse logistic regression: a convex programming approach. IEEE Trans. Inform. Theory 59(1), 482\u2013494 (2013)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"8","key":"19_CR12","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1002\/cpa.20227","volume":"61","author":"M Rudelson","year":"2008","unstructured":"Rudelson, M., Vershynin, R.: On sparse reconstruction from Fourier and Gaussian measurements. Commun. Pure Appl. Math. 61(8), 1025\u20131045 (2008). iav009","journal-title":"Commun. Pure Appl. Math."},{"key":"19_CR13","doi-asserted-by":"crossref","unstructured":"Milman, V.: Surprising geometric phenomena in high-dimensional convexity theory. In: European Congress of Mathematics, pp. 73\u201391. Birkhauser Basel (1998)","DOI":"10.1007\/978-3-0348-8898-1_4"},{"key":"19_CR14","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BFb0081737","volume-title":"Geometric Aspects of Functional Analys","author":"Y Gordon","year":"1988","unstructured":"Gordon, Y.: On Milman\u2019s inequality and random subspaces which escape through a mesh in R n . In: Lindenstrauss, J., Milman, V.D. (eds.) Geometric Aspects of Functional Analys, vol. 1317, pp. 84\u2013106. Springer, Berlin (1988)"},{"issue":"1","key":"19_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0894-0347-08-00600-0","volume":"22","author":"D Donoho","year":"2009","unstructured":"Donoho, D., Tanner, J.: Counting faces of randomly projected polytopes when the projection radically lowers dimension. J. Am. Math. Soc. 22(1), 1\u201353 (2009)","journal-title":"J. Am. Math. Soc."},{"issue":"4","key":"19_CR16","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1007\/s00039-007-0618-7","volume":"17","author":"S Mendelson","year":"2007","unstructured":"Mendelson, S., Pajor, A., Tomczak-Jaegermann, N.: Reconstruction and subgaussian operators in asymptotic geometric analysis. Geometric Func. Anal. 17(4), 1248\u20131282 (2007)","journal-title":"Geometric Func. Anal."},{"key":"19_CR17","unstructured":"Vershynin, R.: Introduction to the non-asymptotic analysis of random matrices (2010). arXiv:1011.3027"},{"key":"19_CR18","unstructured":"Oymak, S., Thrampoulidis, C., Hassibi, B.: Simple bounds for noisy linear inverse problems with exact side information (2013). arXiv:1312.0641"},{"key":"19_CR19","volume-title":"Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations","author":"S Oymak","year":"2015","unstructured":"Oymak, S.: Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations. California Institute of Technology, Pasadena (2015)"},{"issue":"11","key":"19_CR20","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/LSP.2013.2278339","volume":"20","author":"L Condat","year":"2013","unstructured":"Condat, L.: A direct algorithm for 1D total variation denoising. IEEE Signal Proc. Lett. 20(11), 1054\u20131057 (2013)","journal-title":"IEEE Signal Proc. Lett."}],"container-title":["Lecture Notes in Computer Science","Intelligent Computing Theories and Application"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-42294-7_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T18:11:52Z","timestamp":1498327912000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-42294-7_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319422930","9783319422947"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-42294-7_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}