{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:17:54Z","timestamp":1760242674097,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T00:00:00Z","timestamp":1456444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an                                        \u21130 -norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an                                        \u21131 -norm optimization that is convex, has a unique solution, converges quickly and iteratively tends to be an                                        \u21130 -norm problem. More specifically, we employ the arctan function with the parameter                                        \u03c3               \u2265               0                                  in our optimization. This function is Lipschitz continuous and approximates                                        \u21131 -norm and                                        \u21130 -norm for small and large values of \u03c3, respectively. We prove that the set of local optima of our problem is continuous versus \u03c3. Thus, by a gradual increase of \u03c3 in each iteration, we may avoid being trapped in a suboptimal solution. We propose to use the alternating direction method of multipliers (ADMM) for our minimization problem iteratively while increasing \u03c3 exponentially. Our evaluations reveal the superiorities and shortcomings of the proposed method compared to several state-of-the-art methods. We consider such evaluations in different experiments over both synthetic and real hyperspectral data, and the results of our proposed methods reveal the sparsest estimated abundances compared to other competitive algorithms for the subimage of AVIRIS cuprite data.<\/jats:p>","DOI":"10.3390\/rs8030187","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T10:23:39Z","timestamp":1456482219000},"page":"187","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["\u21130-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing"],"prefix":"10.3390","volume":"8","author":[{"given":"Yaser","family":"Esmaeili Salehani","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Walter Light Hall, Queen\u2019s University, Kingston, ON K7L 3N6, Canada"}]},{"given":"Saeed","family":"Gazor","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Walter Light Hall, Queen\u2019s University, Kingston, ON K7L 3N6, Canada"}]},{"given":"Il-Min","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Walter Light Hall, Queen\u2019s University, Kingston, ON K7L 3N6, Canada"}]},{"given":"Shahram","family":"Yousefi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Walter Light Hall, Queen\u2019s University, Kingston, ON K7L 3N6, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/79.974718","article-title":"Hyperspectral image data analysis","volume":"19","author":"Landgrebe","year":"2002","journal-title":"IEEE Signal Process. 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