{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:24:12Z","timestamp":1772252652785,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T00:00:00Z","timestamp":1568851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Czech Science Foundation (GA\u010cR)","award":["17-33798L"],"award-info":[{"award-number":["17-33798L"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.<\/jats:p>","DOI":"10.3390\/axioms8030105","type":"journal-article","created":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T10:55:21Z","timestamp":1568890521000},"page":"105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A New Generalized Projection and Its Application to Acceleration of Audio Declipping"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8381-4442","authenticated-orcid":false,"given":"Pavel","family":"Rajmic","sequence":"first","affiliation":[{"name":"Signal Processing Laboratory, Brno University of Technology, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2221-2058","authenticated-orcid":false,"given":"Pavel","family":"Z\u00e1vi\u0161ka","sequence":"additional","affiliation":[{"name":"Signal Processing Laboratory, Brno University of Technology, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2700-5114","authenticated-orcid":false,"given":"V\u00edt\u011bzslav","family":"Vesel\u00fd","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, 616 69 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1806-5809","authenticated-orcid":false,"given":"Ond\u0159ej","family":"Mokr\u00fd","sequence":"additional","affiliation":[{"name":"Signal Processing Laboratory, Brno University of Technology, 616 00 Brno, Czech Republic"},{"name":"Faculty of Mechanical Engineering, Brno University of Technology, 616 69 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Boyd, S.P., and Vandenberghe, L. 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