{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T19:07:02Z","timestamp":1648753622214},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Data Sci. Adapt. Data Anal."],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p> In this paper, we study the sparse representation of a finite energy signal with intrinsic mode functions in a dictionary consisting of nonlinear Fourier atoms. Each nonlinear Fourier atom is a mono-component with a physically meaningful nonnegative instantaneous frequency. The sparse representation is obtained adaptively by an orthogonal matching pursuit using a two-level greedy search. It is demonstrated that the representation has efficient energy decay in error compared to the Fourier expansion and wavelet expansion. <\/jats:p>","DOI":"10.1142\/s2424922x16500078","type":"journal-article","created":{"date-parts":[[2016,10,6]],"date-time":"2016-10-06T23:33:54Z","timestamp":1475796834000},"page":"1650007","source":"Crossref","is-referenced-by-count":0,"title":["Sparse Representation with Nonlinear Fourier Atoms"],"prefix":"10.1142","volume":"08","author":[{"given":"Bruce W.","family":"Suter","sequence":"first","affiliation":[{"name":"Air Force Research Lab, RI, Rome, NY, USA"}]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Auburn University at Montgomery, Montgomery, AL, USA"}]}],"member":"219","published-online":{"date-parts":[[2016,10,6]]},"reference":[{"key":"S2424922X16500078BIB001","first-page":"417","volume":"80","author":"Boashash B","year":"1992","journal-title":"Proc. IEEE"},{"key":"S2424922X16500078BIB002","volume-title":"Time\u2013Frequency Signal Analysis: Methods and Applications.","author":"Boashash B","year":"1992"},{"key":"S2424922X16500078BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392815"},{"key":"S2424922X16500078BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/00036810903042240"},{"key":"S2424922X16500078BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691310003432"},{"key":"S2424922X16500078BIB007","volume-title":"Time\u2013Frequency Analysis.","author":"Cohen L","year":"1995"},{"key":"S2424922X16500078BIB008","doi-asserted-by":"publisher","DOI":"10.1137\/0806023"},{"key":"S2424922X16500078BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.08.002"},{"key":"S2424922X16500078BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02678430"},{"key":"S2424922X16500078BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/18.119728"},{"key":"S2424922X16500078BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1684(02)00483-8"},{"key":"S2424922X16500078BIB013","volume-title":"Time\u2013Frequency\/Time-Scale Analysis.","author":"Flandrin P","year":"1999"},{"key":"S2424922X16500078BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2012.10.001"},{"key":"S2424922X16500078BIB015","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"S2424922X16500078BIB017","doi-asserted-by":"publisher","DOI":"10.1121\/1.416061"},{"key":"S2424922X16500078BIB018","doi-asserted-by":"publisher","DOI":"10.1109\/78.205756"},{"key":"S2424922X16500078BIB019","volume-title":"A Wavelet Tour of Signal Processing \u2014 The Sparse Way.","author":"Mallat S","year":"2009","edition":"3"},{"key":"S2424922X16500078BIB020","doi-asserted-by":"publisher","DOI":"10.1109\/78.258082"},{"key":"S2424922X16500078BIB021","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112083000579"},{"key":"S2424922X16500078BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2011.71"},{"key":"S2424922X16500078BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/78.558469"},{"key":"S2424922X16500078BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2014.03.014"},{"key":"S2424922X16500078BIB026","volume-title":"Joint Time\u2013Frequency Analysis: Methods and Applications.","author":"Qian S","year":"1996"},{"key":"S2424922X16500078BIB027","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691314610086"},{"key":"S2424922X16500078BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.07.037"},{"key":"S2424922X16500078BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-9091-3_21"},{"key":"S2424922X16500078BIB032","volume-title":"An Introduction to Nonharmonic Fourier Series.","author":"Young R. M.","year":"2001","edition":"1"}],"container-title":["Advances in Data Science and Adaptive Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S2424922X16500078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:50:22Z","timestamp":1565106622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S2424922X16500078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4]]},"references-count":27,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2016,10,6]]},"published-print":{"date-parts":[[2016,4]]}},"alternative-id":["10.1142\/S2424922X16500078"],"URL":"https:\/\/doi.org\/10.1142\/s2424922x16500078","relation":{},"ISSN":["2424-922X","2424-9238"],"issn-type":[{"value":"2424-922X","type":"print"},{"value":"2424-9238","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4]]}}}