{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:45:56Z","timestamp":1760150756636,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T00:00:00Z","timestamp":1703548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Technology Innovation Center for Integrated Applications in Remote Sensing and Navigation","award":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"],"award-info":[{"award-number":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"]}]},{"name":"Ministry of Natural Resources, P.R. China","award":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"],"award-info":[{"award-number":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"]}]},{"name":"Startup Foundation for Introducing Talent of NUIST","award":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"],"award-info":[{"award-number":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"]}]},{"name":"Natural Science Research of the Jiangsu Higher Education Institutions of China","award":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"],"award-info":[{"award-number":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"]}]},{"name":"Major Project of High Resolution Earth Observation System","award":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"],"award-info":[{"award-number":["TICIARSN-2023-02","2022R118","23KJB420003","30-Y60B01-9003-22\/23"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Hyperspectral image (HSIs) denoising is a preprocessing step that plays a crucial role in many applications used in Earth observation missions. Low-rank tensor representation can be utilized to restore mixed-noise HSIs, such as those affected by mixed Gaussian, impulse, stripe, and deadline noises. Although there is a considerable body of research on spatial and spectral prior knowledge concerning subspace, the correlation between the spectral continuity and the nonlocal sparsity of the spectral and spatial factors is not yet fully understood. To address this deficiency, in the present study, we determined the correlation between these factors using a cascaded technique, and we describe in this paper the double-factor tensor cascaded-rank (DFTCR) minimization method that was used. The information existing in the nonlocal sparsity property of the spatial factor was employed to promote a geometrical feature representation, and a tensor cascaded-rank minimization approach was introduced as a nonlocal self-similarity to promote restoration quality. The continuity between the difference and nonlocal gradient sparsity constraints of the spectral factor was also introduced to learn the basis. Furthermore, to estimate the solutions of the proposed model, we developed an algorithm based on the alternating direction method of multipliers (ADMM). The performance of the DFTCR method was tested by a comparison with eleven established denoising methods for HSIs. The results showed that the proposed DFTCR method exhibited superior performance in the removal of mixed noise from HSIs.<\/jats:p>","DOI":"10.3390\/rs16010109","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T02:58:12Z","timestamp":1703645892000},"page":"109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Double-Factor Tensor Cascaded-Rank Decomposition for Hyperspectral Image Denoising"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3376-3592","authenticated-orcid":false,"given":"Jie","family":"Han","sequence":"first","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"Technology Innovation Center for Integration Application in Remote Sensing and Navigation, Ministry of Natural Resources of the People\u2019s Republic of China, Nanjing 210044, China"},{"name":"Jiangsu Engineering Center for Collaborative Navigation Positioning and Smart Applications, Nanjing 210044, China"}]},{"given":"Chuang","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"}]},{"given":"Haiyong","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"Technology Innovation Center for Integration Application in Remote Sensing and Navigation, Ministry of Natural Resources of the People\u2019s Republic of China, Nanjing 210044, China"},{"name":"Jiangsu Engineering Center for Collaborative Navigation Positioning and Smart Applications, Nanjing 210044, China"}]},{"given":"Zhichao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.rse.2003.12.013","article-title":"Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture","volume":"90","author":"Driss","year":"2004","journal-title":"Remote Sens. Environ."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","unstructured":"Shen, F., Zhao, H., Zhu, Q., Sun, X., and Liu, Y. (2021, January 11\u201316). Chinese Hyperspectral Satellite Missions and Preliminary Applications of Aquatic Environment. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9553479"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/TRO.2020.3031214","article-title":"Self-Supervised Visual Terrain Classification from Unsupervised Acoustic Feature Learning","volume":"37","author":"Burgard","year":"2021","journal-title":"IEEE Trans. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"S110","DOI":"10.1016\/j.rse.2007.07.028","article-title":"Recent advances in techniques for hyperspectral image processing","volume":"113","author":"Antonio","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/MSP.2013.2279507","article-title":"Sparsity and Structure in Hyperspectral Imaging: Sensing, Reconstruction, and Target Detection","volume":"31","author":"Willett","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2023.3335418","article-title":"Mixed Noise Removal for Hyperspectral Images Based on Global Tensor Low-Rankness and Nonlocal SVD-Aided Group Sparsity","volume":"61","author":"Sun","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1109\/TIP.2022.3226406","article-title":"Tensor Cascaded-Rank Minimization in Subspace: A Unified Regime for Hyperspectral Image Low-Level Vision","volume":"32","author":"Sun","year":"2023","journal-title":"IEEE Trans. Image Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8743","DOI":"10.1109\/TIP.2021.3120037","article-title":"LR-Net: Low-Rank Spatial-Spectral Network for Hyperspectral Image Denoising","volume":"30","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1109\/TIP.2002.801126","article-title":"On the origin of the bilateral filter and ways to improve it","volume":"11","author":"Elad","year":"2002","journal-title":"IEEE Trans. Image Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","article-title":"Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering","volume":"16","author":"Dabov","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1109\/TIP.2012.2210725","article-title":"Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction","volume":"22","author":"Maggioni","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3952","DOI":"10.1109\/TIP.2012.2199324","article-title":"Video Denoising, Deblocking, and Enhancement Through Separable 4-D Nonlocal Spatiotemporal Transforms","volume":"21","author":"Maggioni","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1080\/07038992.2014.917582","article-title":"Denoising Hyperspectral Imagery Using Principal Component Analysis and Block-Matching 4D Filtering","volume":"40","author":"Chen","year":"2014","journal-title":"Can. J. Remote Sens."},{"key":"ref_16","unstructured":"Buades, A., Coll, B., and Morel, J.-M. (2005, January 20\u201325). A non-local algorithm for image denoising. Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR\u201905), San Diego, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1109\/JSTSP.2018.2873047","article-title":"Robust Tensor Approximation with Laplacian Scale Mixture Modeling for Multiframe Image and Video Denoising","volume":"12","author":"Dong","year":"2018","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3098","DOI":"10.1109\/TIP.2016.2639781","article-title":"Structure-Based Low-Rank Model with Graph Nuclear Norm Regularization for Noise Removal","volume":"26","author":"Ge","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","first-page":"2089","article-title":"Non-Local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration","volume":"44","author":"He","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"10438","DOI":"10.1109\/TGRS.2020.3046038","article-title":"Hyperspectral Image Denoising Based on Global and Nonlocal Low-Rank Factorizations","volume":"59","author":"Zhuang","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2023.3269224","article-title":"Nonlocal Structured Sparsity Regularization Modeling for Hyperspectral Image Denoising","volume":"61","author":"Zha","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","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_23","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_24","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/JSTARS.2012.2232904","article-title":"Hyperspectral Imagery Restoration Using Nonlocal Spectral-Spatial Structured Sparse Representation With Noise Estimation","volume":"6","author":"Qian","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1109\/TGRS.2015.2457614","article-title":"Spectral\u2013Spatial Adaptive Sparse Representation for Hyperspectral Image Denoising","volume":"54","author":"Lu","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2458","DOI":"10.1109\/JSTARS.2013.2272879","article-title":"Hyperspectral Image Denoising Using First Order Spectral Roughness Penalty in Wavelet Domain","volume":"7","author":"Rasti","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_28","first-page":"1","article-title":"Hyperspectral Image Denoising Using Spectral-Spatial Transform-Based Sparse and Low-Rank Representations","volume":"60","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1109\/JSTARS.2018.2796570","article-title":"Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations","volume":"11","author":"Zhuang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","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_31","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_32","doi-asserted-by":"crossref","first-page":"4558","DOI":"10.1109\/TCYB.2020.2983102","article-title":"Weighted Low-Rank Tensor Recovery for Hyperspectral Image Restoration","volume":"50","author":"Chang","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","first-page":"8450","DOI":"10.1109\/TGRS.2020.2987954","article-title":"Double-Factor-Regularized Low-Rank Tensor Factorization for Mixed Noise Removal in Hyperspectral Image","volume":"58","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","first-page":"1","article-title":"Hyperspectral Image Denoising Using Factor Group Sparsity-Regularized Nonconvex Low-Rank Approximation","volume":"60","author":"Chen","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","first-page":"1","article-title":"Fast Hyperspectral Image Denoising and Destriping Method Based on Graph Laplacian Regularization","volume":"61","author":"Su","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","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":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3309","DOI":"10.1109\/TGRS.2020.3007945","article-title":"Hyperspectral Image Restoration via Global L1-2 Spatial\u2013Spectral Total Variation Regularized Local Low-Rank Tensor Recovery","volume":"59","author":"Zeng","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1109\/TGRS.2018.2865197","article-title":"Hyperspectral Image Denoising Employing a Spatial\u2013Spectral Deep Residual Convolutional Neural Network","volume":"57","author":"Yuan","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.isprsjprs.2020.04.010","article-title":"Deep spatio-spectral Bayesian posterior for hyperspectral image non-i.i.d. noise removal","volume":"164","author":"Zhang","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2516","DOI":"10.1109\/TGRS.2019.2952062","article-title":"A Single Model CNN for Hyperspectral Image Denoising","volume":"58","author":"Maffei","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"104531","DOI":"10.1016\/j.infrared.2022.104531","article-title":"Attention based deep convolutional U-Net with CSA optimization for hyperspectral image denoising","volume":"129","author":"Murugesan","year":"2023","journal-title":"Infrared Phys. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1109\/TGRS.2018.2859203","article-title":"HSI-DeNet: Hyperspectral Image Restoration via Convolutional Neural Network","volume":"57","author":"Chang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02289464","article-title":"Some mathematical notes on three-mode factor analysis","volume":"31","author":"Tucker","year":"1966","journal-title":"Psychometrika"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF02310791","article-title":"Analysis of individual differences in multidimensional scaling via an n-way generalization of \u201cEckart-Young\u201d decomposition","volume":"35","author":"Carroll","year":"1970","journal-title":"Psychometrika"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1137\/110837711","article-title":"Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging","volume":"34","author":"Kilmer","year":"2013","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Ely, G., Aeron, S., Hao, N., and Kilmer, M. (2014, January 23\u201328). Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD. Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.485"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.1137\/090752286","article-title":"Tensor-Train Decomposition","volume":"33","author":"Oseledets","year":"2011","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_49","unstructured":"Zhao, Q., Zhou, G., Xie, S., Zhang, L., and Cichocki, A. (2016). Tensor Ring Decomposition. arXiv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MGRS.2022.3227063","article-title":"Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A comprehensive review","volume":"11","author":"Wang","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_51","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":"2011","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TPAMI.2017.2689021","article-title":"A Unified Alternating Direction Method of Multipliers by Majorization Minimization","volume":"40","author":"Lu","year":"2018","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_53","first-page":"1","article-title":"Hyperspectral Image Denoising Using Nonconvex Fraction Function","volume":"20","author":"Liu","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/1\/109\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:42:21Z","timestamp":1760132541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/1\/109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,26]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["rs16010109"],"URL":"https:\/\/doi.org\/10.3390\/rs16010109","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,12,26]]}}}