{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:55:20Z","timestamp":1740142520524,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T00:00:00Z","timestamp":1714780800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T00:00:00Z","timestamp":1714780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100016150","name":"Fondation OCP","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100016150","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s40314-024-02749-9","type":"journal-article","created":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T12:01:47Z","timestamp":1714824107000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Tensor sparse representation via Einstein product"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-5869-7586","authenticated-orcid":false,"given":"Ferdaous Ait","family":"Addi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdeslem Hafid","family":"Bentbib","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalide","family":"Jbilou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,4]]},"reference":[{"key":"2749_CR1","doi-asserted-by":"crossref","unstructured":"Beik FPA, Movahed FS, Ahmadi-Asl S (2016) on the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations. Numer Linear Algebra Appl 23(3):444\u2013466","DOI":"10.1002\/nla.2033"},{"issue":"2","key":"2749_CR2","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1137\/100804577","volume":"34","author":"M Brazell","year":"2013","unstructured":"Brazell M, Li N, Navasca C, Tamon C (2013) Solving multilinear systems via tensor inversion. SIAM J Matrix Anal Appl 34(2):542\u2013570","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"1","key":"2749_CR3","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1162\/NECO_a_00385","volume":"25","author":"CF Caiafa","year":"2013","unstructured":"Caiafa CF, Cichocki A (2013) Computing sparse representations of multidimensional signals using Kronecker bases. Neural Comput 25(1):186\u2013220","journal-title":"Neural Comput"},{"issue":"6","key":"2749_CR4","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1002\/widm.1108","volume":"3","author":"CF Caiafa","year":"2013","unstructured":"Caiafa CF, Cichocki A (2013) Multidimensional compressed sensing and their applications. Wiley Interdiscip Rev Data Min Knowl Discov 3(6):355\u2013380","journal-title":"Wiley Interdiscip Rev Data Min Knowl Discov"},{"key":"2749_CR5","doi-asserted-by":"crossref","unstructured":"Candes J EJ, Romberg Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489\u2013509","DOI":"10.1109\/TIT.2005.862083"},{"issue":"12","key":"2749_CR6","doi-asserted-by":"publisher","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"EJ Candes","year":"2005","unstructured":"Candes EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203\u20134215","journal-title":"IEEE Trans Inf Theory"},{"issue":"1","key":"2749_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1137\/S1064827596304010","volume":"20","author":"SS Chen","year":"1998","unstructured":"Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20(1):33\u201361","journal-title":"SIAM J Sci Comput"},{"issue":"3","key":"2749_CR8","doi-asserted-by":"publisher","first-page":"1033","DOI":"10.1137\/070690729","volume":"30","author":"L De Lathauwer","year":"2008","unstructured":"De Lathauwer L (2008) Decompositions of a higher-order tensor in block terms-Part II: definitions and uniqueness. SIAM J Matrix Anal Appl 30(3):1033\u20131066","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"4","key":"2749_CR9","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289\u20131306","journal-title":"IEEE Trans Inf Theory"},{"issue":"11","key":"2749_CR10","doi-asserted-by":"publisher","first-page":"4789","DOI":"10.1109\/TIT.2008.929958","volume":"54","author":"DL Donoho","year":"2008","unstructured":"Donoho DL, Tsaig Y (2008) Fast solution of l1\u2014norm minimization problems when the solution may be sparse. IEEE Trans Inf Theory 54(11):4789\u20134812","journal-title":"IEEE Trans Inf Theory"},{"key":"2749_CR11","doi-asserted-by":"crossref","unstructured":"Duarte MF, Baraniuk RG (2010) Kronecker product matrices for compressive sensing. In: 2010 IEEE international conference on acoustics, speech, and signal processing, ICASSP 2010\u2014proceedings, pp 3650\u20133653","DOI":"10.1109\/ICASSP.2010.5495900"},{"issue":"2","key":"2749_CR12","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1214\/009053604000000067","volume":"32","author":"B Efron","year":"2004","unstructured":"Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2):407\u2013499","journal-title":"Ann Stat"},{"key":"2749_CR13","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.apnum.2022.06.010","volume":"181","author":"M El Guide","year":"2022","unstructured":"El Guide M, El Ichi A, Jbilou K, Beik FPA (2022) Tensor Krylov subspace methods via the Einstein product with applications to image and video processing. Appl Numer Math 181:347\u2013363","journal-title":"Appl Numer Math"},{"key":"2749_CR14","volume-title":"A mathematical introduction to compressive sensing. Applied and numerical harmonic analysis","author":"S Foucart","year":"2013","unstructured":"Foucart S, Rauhut H (2013) A mathematical introduction to compressive sensing. Applied and numerical harmonic analysis. Springer, New York"},{"key":"2749_CR15","doi-asserted-by":"crossref","unstructured":"Kolda T (2006) Multilinear operators for higher-order decompositions. In: Technical report SAND2006-2081, 923081, Sandia National Laboratories. https:\/\/www.osti.gov\/servlets\/purl\/923081\/","DOI":"10.2172\/923081"},{"issue":"3","key":"2749_CR16","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51(3):455\u2013500","journal-title":"SIAM Rev"},{"key":"2749_CR17","doi-asserted-by":"crossref","unstructured":"Li Q, Schonfeld D, Friedland S (2013) Generalized tensor compressive sensing. In: 2013 IEEE international conference on multimedia and expo (ICME), pp 1\u20136","DOI":"10.1109\/ICME.2013.6607560"},{"key":"2749_CR18","doi-asserted-by":"crossref","unstructured":"Qi N, Shi Y, Sun X, Yin B (2016) Tensr: multi-dimensional tensor sparse representation. In: 2016 IEEE conference on computer vision and pattern recognition (CVPR), pp 5916\u20135925","DOI":"10.1109\/CVPR.2016.637"},{"issue":"10","key":"2749_CR19","doi-asserted-by":"publisher","first-page":"2231","DOI":"10.1109\/TIT.2004.834793","volume":"50","author":"JA Tropp","year":"2004","unstructured":"Tropp JA (2004) Greed is good: algorithmic results for sparse approximation. IEEE Trans Inf Theory 50(10):2231\u20132242","journal-title":"IEEE Trans Inf Theory"},{"issue":"3","key":"2749_CR20","first-page":"502","volume":"66","author":"R Zhao","year":"2019","unstructured":"Zhao R, Wang Q (2019) Learning separable dictionaries for sparse tensor representation: an online approach. IEEE Trans Circuits Syst II Exp Briefs 66(3):502\u2013506","journal-title":"IEEE Trans Circuits Syst II Exp Briefs"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02749-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02749-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02749-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T02:02:58Z","timestamp":1718071378000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02749-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,4]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2749"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02749-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,5,4]]},"assertion":[{"value":"13 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest that could have influenced the work presented in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"222"}}