{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:22:54Z","timestamp":1772151774681,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61701337"],"award-info":[{"award-number":["61701337"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671382"],"award-info":[{"award-number":["61671382"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin City","doi-asserted-by":"publisher","award":["18JCQNJC01600"],"award-info":[{"award-number":["18JCQNJC01600"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Spectral unmixing of hyperspectral images is an important issue in the fields of remote sensing. Jointly exploring the spectral and spatial information embedded in the data is helpful to enhance the consistency between mixing\/unmixing models and real scenarios. This paper proposes a graph regularized nonlinear unmixing method based on the recent multilinear mixing model (MLM). The MLM takes account of all orders of interactions between endmembers, and indicates the pixel-wise nonlinearity with a single probability parameter. By incorporating the Laplacian graph regularizers, the proposed method exploits the underlying manifold structure of the pixels\u2019 spectra, in order to augment the estimations of both abundances and nonlinear probability parameters. Besides the spectrum-based regularizations, the sparsity of abundances is also incorporated for the proposed model. The resulting optimization problem is addressed by using the alternating direction method of multipliers (ADMM), yielding the so-called graph regularized MLM (G-MLM) algorithm. To implement the proposed method on large hypersepectral images in real world, we propose to utilize a superpixel construction approach before unmixing, and then apply G-MLM on each superpixel. The proposed methods achieve superior unmixing performances to state-of-the-art strategies in terms of both abundances and probability parameters, on both synthetic and real datasets.<\/jats:p>","DOI":"10.3390\/rs11192188","type":"journal-article","created":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T10:48:14Z","timestamp":1568976494000},"page":"2188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Graph Regularized Multilinear Mixing Model for Nonlinear Hyperspectral Unmixing"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2051-9905","authenticated-orcid":false,"given":"Minglei","family":"Li","sequence":"first","affiliation":[{"name":"Center for Applied Mathematics, Tianjin University, Tianjin 300072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8113-3707","authenticated-orcid":false,"given":"Fei","family":"Zhu","sequence":"additional","affiliation":[{"name":"Center for Applied Mathematics, Tianjin University, Tianjin 300072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9550-3633","authenticated-orcid":false,"given":"Alan J. X.","family":"Guo","sequence":"additional","affiliation":[{"name":"Center for Applied Mathematics, Tianjin University, Tianjin 300072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2306-8860","authenticated-orcid":false,"given":"Jie","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2018an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/JSTARS.2012.2194696","article-title":"Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches","volume":"5","author":"Plaza","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. 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