{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:31:20Z","timestamp":1772296280180,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,2,15]],"date-time":"2016-02-15T00:00:00Z","timestamp":1455494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>In hyperspectral images, once the pure spectra of the materials are known, hyperspectral unmixing seeks to find their relative abundances throughout the scene. We present a novel variational model for hyperspectral unmixing from incomplete noisy data, which combines a spatial regularity prior with the knowledge of the pure spectra. The material abundances are found by minimizing the resulting convex functional with a primal dual algorithm. This extends least squares unmixing to the case of incomplete data, by using total variation regularization and masking of unknown data. Numerical tests with artificial and real-world data demonstrate that our method successfully recovers the true mixture coefficients from heavily-corrupted data.<\/jats:p>","DOI":"10.3390\/jimaging2010007","type":"journal-article","created":{"date-parts":[[2016,2,15]],"date-time":"2016-02-15T06:23:07Z","timestamp":1455517387000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hyperspectral Unmixing from Incomplete and Noisy Data"],"prefix":"10.3390","volume":"2","author":[{"given":"Martin","family":"Montag","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany"},{"name":"Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henrike","family":"Stephani","sequence":"additional","affiliation":[{"name":"Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1080\/01431169308904402","article-title":"Linear Mixing and the Estimation of Ground Cover Proportions","volume":"14","author":"Settle","year":"1993","journal-title":"Int. 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