{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T07:12:35Z","timestamp":1768893155519,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shaanxi Key R &amp; D Plan","award":["2020ZDLGY07-11"],"award-info":[{"award-number":["2020ZDLGY07-11"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771391"],"award-info":[{"award-number":["61771391"]}],"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":["61371152"],"award-info":[{"award-number":["61371152"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shenzhen Municipal Science and Technology Innovation Committee","award":["JCYJ20170815162956949"],"award-info":[{"award-number":["JCYJ20170815162956949"]}]},{"name":"Shenzhen Municipal Science and Technology Innovation Committee","award":["JCYJ20180306171146740"],"award-info":[{"award-number":["JCYJ20180306171146740"]}]},{"name":"the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University","award":["CX201917"],"award-info":[{"award-number":["CX201917"]}]},{"name":"the natural science basic research plan in Shaanxi Province of China","award":["No. 2018JM6056"],"award-info":[{"award-number":["No. 2018JM6056"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>To eliminate the mixed noise in hyperspectral images (HSIs), three-dimensional total variation (3DTV) regularization has been proven as an efficient tool. However, 3DTV regularization is prone to losing image details in restoration. To resolve this issue, we proposed a novel TV, named spatial domain spectral residual total variation (SSRTV). Considering that there is much residual texture information in spectral variation image, SSRTV first calculates the difference between the pixel values of adjacent bands and then calculates a 2DTV for the residual image. Experimental results demonstrated that the SSRTV regularization term is powerful at changing the structures of noises in an original HSI, thus allowing low-rank techniques to get rid of mixed noises more efficiently without treating them as low-rank features. The global low-rankness and spatial\u2013spectral correlation of HSI is exploited by low-rank Tucker decomposition (LRTD). Moreover, it was demonstrated that the l2,1 norm is more effective to deal with sparse noise, especially the sample-specific noise such as stripes or deadlines. The augmented Lagrange multiplier (ALM) algorithm was adopted to solve the proposed model. Finally, experimental results with simulated and real data illustrated the validity of the proposed method. The proposed method outperformed state-of-the-art TV-regularized low-rank matrix\/tensor decomposition methods in terms of quantitative metrics and visual inspection.<\/jats:p>","DOI":"10.3390\/rs14030511","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:34:40Z","timestamp":1642970080000},"page":"511","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Hyperspectral Image Restoration via Spatial-Spectral Residual Total Variation Regularized Low-Rank Tensor Decomposition"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1668-4318","authenticated-orcid":false,"given":"Xiangyang","family":"Kong","sequence":"first","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Department of Basic Education, Sichuan Engineering Technical College, Deyang 618000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6974-7327","authenticated-orcid":false,"given":"Yongqiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3741-1124","authenticated-orcid":false,"given":"Jonathan Cheung-Wai","family":"Chan","sequence":"additional","affiliation":[{"name":"Department of Electronics and Informatics, Vrije Universiteit Brussel, 1050 Brussel, Belgium"}]},{"given":"Jize","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,21]]},"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. Remote Sens. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1109\/TGRS.2013.2284280","article-title":"Hyperspectral Image Restoration Using Low-Rank Matrix Recovery","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6983","DOI":"10.1080\/01431161.2013.804225","article-title":"A novel l 1\/2 sparse regression method for hyperspectral unmixing","volume":"34","author":"Sun","year":"2013","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sun, L., Wang, S., Wang, J., Zheng, Y., and Jeon, B. (2017). Hyperspectral classification employing spatial\u2013spectral low rank representation in hidden fields. J. Ambient. Intell. Humaniz. Comput., 1\u201312.","DOI":"10.1007\/s12652-017-0586-1"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1109\/JSTARS.2017.2755639","article-title":"GPU Parallel Implementation of Spatially Adaptive Hyperspectral Image Classification","volume":"11","author":"Wu","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1990","DOI":"10.1109\/TGRS.2015.2493201","article-title":"Anomaly Detection in Hyperspectral Images Based on Low-Rank and Sparse Representation","volume":"54","author":"Xu","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bollenbeck, F., Backhaus, A., and Seiffert, U. (2011, January 6\u20139). A multivariate wavelet-PCA denoising-filter for hyperspectral images. Proceedings of the 2011 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Lisbon, Portugal.","DOI":"10.1109\/WHISPERS.2011.6080901"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Heo, A., Lee, J.-H., Choi, E.-J., Choi, W.-C., Kim, S.H., and Park, D.-J. (2011, January 20). Noise reduction of hyperspectral images using a joint bilateral filter with fused images. Proceedings of the SPIE\u2014The International Society for Optical Engineering, Orlando, FL, USA.","DOI":"10.1117\/12.884359"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3717","DOI":"10.1109\/TGRS.2012.2187063","article-title":"Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis","volume":"50","author":"Liu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/36.3001","article-title":"A transformation for ordering multispectral data in terms of image quality with implications for noise removal","volume":"26","author":"Green","year":"1988","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1109\/TIP.2006.881969","article-title":"Image denoising via sparse and redundant representations over learned dictionaries","volume":"15","author":"Elad","year":"2006","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1109\/JSTARS.2017.2779539","article-title":"Hyperspectral Image Restoration Via Total Variation Regularized Low-Rank Tensor Decomposition","volume":"11","author":"Wang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/JSTSP.2011.2132692","article-title":"Noise Reduction of Hyperspectral Images Using Kernel Non-Negative Tucker Decomposition","volume":"5","author":"Karami","year":"2011","journal-title":"IEEE J. Sel. Top. Signal Processing"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Peng, Y., Meng, D., Xu, Z., Gao, C., Yang, Y., and Zhang, B. (2014, January 24\u201327). Decomposable Nonlocal Tensor Dictionary Learning for Multispectral Image Denoising. Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.377"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/TGRS.2005.860982","article-title":"Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage","volume":"44","author":"Othman","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/TGRS.2014.2321557","article-title":"Hyperspectral Image Denoising via Sparse Representation and Low-Rank Constraint","volume":"53","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3660","DOI":"10.1109\/TGRS.2012.2185054","article-title":"Hyperspectral Image Denoising Employing a Spectral\u2013Spatial Adaptive Total Variation Model","volume":"50","author":"Yuan","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5366","DOI":"10.1109\/TGRS.2017.2706326","article-title":"Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation","volume":"55","author":"Chen","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4642","DOI":"10.1109\/TGRS.2016.2547879","article-title":"Hyperspectral image restoration via iteratively regularized weighted Schatten p-norm minimization","volume":"54","author":"Xie","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4842","DOI":"10.1109\/TIP.2016.2599290","article-title":"Weighted Schatten p-norm minimization for image denoising and background subtraction","volume":"25","author":"Xie","year":"2016","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TGRS.2015.2452812","article-title":"Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration","volume":"54","author":"He","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1109\/TGRS.2018.2875304","article-title":"Hyperspectral Image Denoising by Fusing the Selected Related Bands","volume":"57","author":"Zheng","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","first-page":"442","article-title":"Hyperspectral Image Denoising Using Spatio-Spectral Total Variation","volume":"13","author":"Aggarwal","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/JSTARS.2018.2800701","article-title":"Hyperspectral Image Denoising Using Local Low-Rank Matrix Recovery and Global Spatial\u2013Spectral Total Variation","volume":"11","author":"He","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27172","DOI":"10.1109\/ACCESS.2017.2768580","article-title":"A Novel Weighted Cross Total Variation Method for Hyperspectral Image Mixed Denoising","volume":"5","author":"Sun","year":"2017","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6196","DOI":"10.1109\/TGRS.2018.2833473","article-title":"Spatial\u2013Spectral Total Variation Regularized Low-Rank Tensor Decomposition for Hyperspectral Image Denoising","volume":"56","author":"Fan","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1109\/ACCESS.2017.2778947","article-title":"Hyperspectral Image Denoising With Group Sparse and Low-Rank Tensor Decomposition","volume":"6","author":"Huang","year":"2017","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Takeyama, S., Ono, S., and Kumazawa, I. (2019, January 22\u201325). Mixed Noise Removal for Hyperspectral Images Using Hybrid Spatio-Spectral Total Variation. Proceedings of the 2019 IEEE International Conference on Image Processing (ICIP), Taipei, Taiwan.","DOI":"10.1109\/ICIP.2019.8803239"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3815","DOI":"10.1109\/TGRS.2014.2385082","article-title":"Spectral\u2013Spatial Kernel Regularized for Hyperspectral Image Denoising","volume":"53","author":"Yuan","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","article-title":"Tensor Decompositions and Applications","volume":"51","author":"Kolda","year":"2009","journal-title":"SIAM Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"803","DOI":"10.4208\/cicp.OA-2016-0074","article-title":"Multiplicative Noise Removal Based on Unbiased Box-Cox Transformation","volume":"22","author":"Huang","year":"2017","journal-title":"Commun. Comput. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3556","DOI":"10.1109\/TCYB.2019.2936042","article-title":"Hyperspectral Image Restoration Using Weighted Group Sparsity-Regularized Low-Rank Tensor Decomposition","volume":"50","author":"Chen","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3062","DOI":"10.1109\/JSTARS.2014.2370062","article-title":"Spectral Nonlocal Restoration of Hyperspectral Images With Low-Rank Property","volume":"8","author":"Zhu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3050","DOI":"10.1109\/JSTARS.2015.2398433","article-title":"Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation","volume":"8","author":"He","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3047","DOI":"10.1109\/TIT.2011.2173156","article-title":"Robust PCA via Outlier Pursuit","volume":"58","author":"Xu","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","article-title":"Robust Recovery of Subspace Structures by Low-Rank Representation","volume":"35","author":"Liu","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_37","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. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers","volume":"3","author":"Boyd","year":"2010","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1049\/iet-spr.2018.5086","article-title":"Singular spectral analysis-based denoising without computing singular values via augmented Lagrange multiplier algorithm","volume":"13","author":"Feng","year":"2019","journal-title":"IET Signal Processing"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.sigpro.2017.06.012","article-title":"Low rank constraint and spatial spectral total variation for hyperspectral image mixed denoising","volume":"142","author":"Wang","year":"2018","journal-title":"Signal Processing"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image Quality Assessment: From Error Visibility to Structural Similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Kong, X., Zhao, Y., Xue, J., Chan, J.C.-W., and Kong, S.G. (2020). Global and Local Tensor Sparse Approximation Models for Hyperspectral Image Destriping. Remote Sens., 12.","DOI":"10.3390\/rs12040704"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4039","DOI":"10.1109\/TGRS.2016.2535458","article-title":"Hyperspectral Image Classification via Basic Thresholding Classifier","volume":"54","author":"Toksoz","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2435","DOI":"10.1109\/TGRS.2008.918089","article-title":"Hyperspectral Subspace Identification","volume":"46","author":"Nascimento","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/511\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:05:26Z","timestamp":1760133926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,21]]},"references-count":44,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["rs14030511"],"URL":"https:\/\/doi.org\/10.3390\/rs14030511","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,21]]}}}