{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T22:08:12Z","timestamp":1761948492353,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T00:00:00Z","timestamp":1561680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006595","name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","doi-asserted-by":"publisher","award":["project number 17PCCDI\/2018 within PNCDI III"],"award-info":[{"award-number":["project number 17PCCDI\/2018 within PNCDI III"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The     \u2113 1     relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through an affine term from one iteration to the next (i.e., the problem\u2019s structure remains the same while only the current vector, which is to be (co)sparsely represented, changes). We exploit this fact by providing an explicit, piecewise affine with a polyhedral support, representation of the solution. Consequently, at runtime, the optimal solution (the (co)sparse representation) is obtained through a simple enumeration throughout the non-overlapping regions of the polyhedral partition and the application of an affine law. We show that, for a suitably large number of parameter instances, the explicit approach outperforms the classical implementation.<\/jats:p>","DOI":"10.3390\/a12070131","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T11:20:26Z","timestamp":1561720826000},"page":"131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Aiding Dictionary Learning Through Multi-Parametric Sparse Representation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4550-9113","authenticated-orcid":false,"given":"Florin","family":"Stoican","sequence":"first","affiliation":[{"name":"Department of Automatic Control and Computers, University Politehnica of Bucharest, 313 Spl. Independen\u021bei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7541-4334","authenticated-orcid":false,"given":"Paul","family":"Irofti","sequence":"additional","affiliation":[{"name":"The Research Institute of the University of Bucharest (ICUB) and Department of Computer Science, University of Bucharest, Bulevardul M. Kog\u0103lniceanu 36-46, 050107 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Elad, M. (2010). Sparse and Redundant Representations: From Theory To Applications in Signal and Image Processing, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-7011-4"},{"key":"ref_2","unstructured":"Fletcher, R. (2013). 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