{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T16:12:46Z","timestamp":1762272766125,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,4,11]],"date-time":"2021-04-11T00:00:00Z","timestamp":1618099200000},"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":["61773316","U1864204"],"award-info":[{"award-number":["61773316","U1864204"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2018KJXX-024"],"award-info":[{"award-number":["2018KJXX-024"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Recently, non-negative tensor factorization (NTF) as a very powerful tool has attracted the attention of researchers. It is used in the unmixing of hyperspectral images (HSI) due to its excellent expression ability without any information loss when describing data. However, most of the existing unmixing methods based on NTF fail to fully explore the unique properties of data, for example, low rank, that exists in both the spectral and spatial domains. To explore this low-rank structure, in this paper we learn the different low-rank representations of HSI in the spectral, spatial and non-local similarity modes. Firstly, HSI is divided into many patches, and these patches are clustered multiple groups according to the similarity. Each similarity group can constitute a 4-D tensor, including two spatial modes, a spectral mode and a non-local similarity mode, which has strong low-rank properties. Secondly, a low-rank regularization with logarithmic function is designed and embedded in the NTF framework, which simulates the spatial, spectral and non-local similarity modes of these 4-D tensors. In addition, the sparsity of the abundance tensor is also integrated into the unmixing framework to improve the unmixing performance through the L2,1 norm. Experiments on three real data sets illustrate the stability and effectiveness of our algorithm compared with five state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/rs13081473","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T05:52:00Z","timestamp":1618206720000},"page":"1473","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Sparse Constrained Low Tensor Rank Representation Framework for Hyperspectral Unmixing"],"prefix":"10.3390","volume":"13","author":[{"given":"Le","family":"Dong","sequence":"first","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yuan","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7894","DOI":"10.1109\/TGRS.2019.2917161","article-title":"A Feature Aggregation Convolutional Neural Network for Remote Sensing Scene Classification","volume":"57","author":"Lu","year":"2019","journal-title":"IEEE Trans. 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