{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:49:27Z","timestamp":1760233767105,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"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>We introduce a novel regularization function for hyperspectral image (HSI), which is based on the nuclear norms of gradient images. Unlike conventional low-rank priors, we achieve a gradient-based low-rank approximation by minimizing the sum of nuclear norms associated with rotated planes in the gradient of a HSI. Our method explicitly and simultaneously exploits the correlation in the spectral domain as well as the spatial domain. Our method exploits the low-rankness of a global region to enhance the dimensionality reduction by the prior. Since our method considers the low-rankness in the gradient domain, it more sensitively detects anomalous variations. Our method achieves high-fidelity image recovery using a single regularization function without the explicit use of any sparsity-inducing priors such as \u21130, \u21131 and total variation (TV) norms. We also apply this regularization to a gradient-based robust principal component analysis and show its superiority in HSI decomposition. To demonstrate, the proposed regularization is validated on a variety of HSI reconstruction\/decomposition problems with performance comparisons to state-of-the-art methods its superior performance.<\/jats:p>","DOI":"10.3390\/rs13040819","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T20:19:36Z","timestamp":1614111576000},"page":"819","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["TNNG: Total Nuclear Norms of Gradients for Hyperspectral Image Prior"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2326-6827","authenticated-orcid":false,"given":"Ryota","family":"Yuzuriha","sequence":"first","affiliation":[{"name":"Information and Computer Science, Graduate School of Science and Engineering, Doshisha University, Kyoto 610-0394, Japan"}]},{"given":"Ryuji","family":"Kurihara","sequence":"additional","affiliation":[{"name":"Xacti Corporation, Osaka 531-6028, Japan"}]},{"given":"Ryo","family":"Matsuoka","sequence":"additional","affiliation":[{"name":"Faculty of Environmental Engineering, The University of Kitakyushu, Kitakyushu 808-0135, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3245-2672","authenticated-orcid":false,"given":"Masahiro","family":"Okuda","sequence":"additional","affiliation":[{"name":"Faculty of Science and Engineering, Doshisha University, Kyoto 610-0394, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/MGRS.2017.2762087","article-title":"Advances in hyperspectral image and signal processing: A comprehensive overview of the state of the art","volume":"5","author":"Ghamisi","year":"2017","journal-title":"IEEE Geosci. 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