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The endmember extraction method is powerful in enhancing spatial structure information for hyperspectral anomaly detection, whereas most approaches are based on matrix representation, which inevitably destroys the spatial or spectral information. In this paper, we treated the hyperspectral image as a third-order tensor and proposed a novel anomaly detection method based on a low-rank linear mixing model of the scene background. The obtained abundance maps possessed more distinctive features than the raw data, which was beneficial for identifying anomalies in the background. Specifically, the low-rank tensor background was approximated as the mode-3 product of an abundance tensor and endmember matrix. Due to the distinctive features of the background\u2019s abundance maps, we characterized them by tensor regularization and imposed low rankness through CP decomposition, smoothness, and sparsity. In addition, we utilized the \u21131,1,2-norm to characterize the tube-wise sparsity of the anomaly, since it accounted for a small portion of the scene. The experimental results obtained using five real datasets demonstrated the outstanding performance of our proposed method.<\/jats:p>","DOI":"10.3390\/rs15061679","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T02:36:22Z","timestamp":1679366182000},"page":"1679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Hyperspectral Anomaly Detection Based on Regularized Background Abundance Tensor Decomposition"],"prefix":"10.3390","volume":"15","author":[{"given":"Wenting","family":"Shang","sequence":"first","affiliation":[{"name":"Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7258-0935","authenticated-orcid":false,"given":"Mohamad","family":"Jouni","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000 Grenoble, France"}]},{"given":"Zebin","family":"Wu","sequence":"additional","affiliation":[{"name":"Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Yang","family":"Xu","sequence":"additional","affiliation":[{"name":"Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9656-9087","authenticated-orcid":false,"given":"Mauro","family":"Dalla Mura","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000 Grenoble, France"},{"name":"Institut Universitaire de France (IUF), 75231 Paris, France"}]},{"given":"Zhihui","family":"Wei","sequence":"additional","affiliation":[{"name":"Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2244672","article-title":"Hyperspectral Remote Sensing Data Analysis and Future Challenges","volume":"1","author":"Plaza","year":"2013","journal-title":"IEEE Geosci. 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