{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T15:25:57Z","timestamp":1784301957734,"version":"3.55.0"},"reference-count":54,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"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":["42001287"],"award-info":[{"award-number":["42001287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"HKRGC GRF","award":["12306616, 12200317, 12300218, 12300519, 17201020"],"award-info":[{"award-number":["12306616, 12200317, 12300218, 12300519, 17201020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The ever-increasing spectral resolution of hyperspectral images (HSIs) is often obtained at the cost of a decrease in the signal-to-noise ratio (SNR) of the measurements. The decreased SNR reduces the reliability of measured features or information extracted from HSIs, thus calling for effective denoising techniques. This work aims to estimate clean HSIs from observations corrupted by mixed noise (containing Gaussian noise, impulse noise, and dead-lines\/stripes) by exploiting two main characteristics of hyperspectral data, namely low-rankness in the spectral domain and high correlation in the spatial domain. We take advantage of the spectral low-rankness of HSIs by representing spectral vectors in an orthogonal subspace, which is learned from observed images by a new method. Subspace representation coefficients of HSIs are learned by solving an optimization problem plugged with an image prior extracted from a neural denoising network. The proposed method is evaluated on simulated and real HSIs. An exhaustive array of experiments and comparisons with state-of-the-art denoisers were carried out.<\/jats:p>","DOI":"10.3390\/rs13204098","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T21:48:39Z","timestamp":1634161719000},"page":"4098","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Hyperspectral Image Mixed Noise Removal Using Subspace Representation and Deep CNN Image Prior"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9622-6535","authenticated-orcid":false,"given":"Lina","family":"Zhuang","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, China"},{"name":"Shenzhen Institute of Research and Innovation, The University of Hong Kong, Shenzhen 518057, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6833-5227","authenticated-orcid":false,"given":"Michael K.","family":"Ng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2936-2681","authenticated-orcid":false,"given":"Xiyou","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China"},{"name":"MNR Key Laboratory for Geo-Environmental Monitoring of Great Bay Area, Shenzhen University, Shenzhen 518060, China"},{"name":"SZU Branch, Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,13]]},"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. Remote Sens."},{"key":"ref_2","first-page":"49","article-title":"Exploring for onshore oil seeps with hyperspectral imaging","volume":"99","author":"Ellis","year":"2001","journal-title":"Oil Gas J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1186\/s13007-017-0233-z","article-title":"Hyperspectral image analysis techniques for the detection and classification of the early onset of plant disease and stress","volume":"13","author":"Lowe","year":"2017","journal-title":"Plant Methods"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Abdellatif, M., Peel, H., Cohn, A.G., and Fuentes, R. (2020). Pavement Crack Detection from Hyperspectral Images Using a Novel Asphalt Crack Index. Remote Sens., 12.","DOI":"10.3390\/rs12183084"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1109\/LGRS.2013.2285124","article-title":"Simultaneous destriping and denoising for remote sensing images with unidirectional total variation and sparse representation","volume":"11","author":"Chang","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Xie, Q., Zhao, Q., Meng, D., Xu, Z., Gu, S., Zuo, W., and Zhang, L. (2016, January 27\u201330). Multispectral images denoising by intrinsic tensor sparsity regularization. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.187"},{"key":"ref_7","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_8","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_9","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":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1049\/el:20071417","article-title":"Hybrid Fourier-wavelet image denoising","volume":"43","author":"Jiang","year":"2007","journal-title":"Electron. Lett."},{"key":"ref_11","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":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6196","DOI":"10.1109\/TGRS.2018.2833473","article-title":"Spatial-spectral 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_13","unstructured":"Chang, Y., Yan, L., and Zhong, S. Hyper-laplacian regularized unidirectional low-rank tensor recovery for multispectral image denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TIP.2019.2926736","article-title":"Hyperspectral Images Denoising via Nonconvex Regularized Low-Rank and Sparse Matrix Decomposition","volume":"29","author":"Xie","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","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":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1109\/TGRS.2020.2993631","article-title":"Hyperspectral Image Mixed Noise Removal Based on Multidirectional Low-Rank Modeling and Spatial\u2013Spectral Total Variation","volume":"59","author":"Wang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhuang, L., Fu, X., Ng, M.K., and Bioucas-Dias, J.M. (2021). Hyperspectral Image Denoising Based on Global and Nonlocal Low-Rank Factorizations. IEEE Trans. Geosci. Remote. Sens.","DOI":"10.1109\/TGRS.2020.3046038"},{"key":"ref_18","unstructured":"He, W., Yao, Q., Li, C., Yokoya, N., and Zhao, Q. Non-Local Meets Global: An Integrated Paradigm for Hyperspectral Denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhuang, L., Gao, L., Zhang, B., Fu, X., and Bioucas-Dias, J.M. (2020). Hyperspectral image denoising and anomaly detection based on low-rank and sparse representations. IEEE Trans. Geosci. Remote. Sens.","DOI":"10.1109\/TGRS.2020.3040221"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7739","DOI":"10.1109\/TGRS.2020.3032168","article-title":"A Tensor Subspace Representation-Based Method for Hyperspectral Image Denoising","volume":"59","author":"Lin","year":"2020","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/JSTARS.2019.2896031","article-title":"Hyperspectral image denoising via subspace-based nonlocal low-rank and sparse factorization","volume":"12","author":"Cao","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","article-title":"Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising","volume":"26","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4608","DOI":"10.1109\/TIP.2018.2839891","article-title":"FFDNet: Toward a fast and flexible solution for CNN-based image denoising","volume":"27","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Guo, S., Yan, Z., Zhang, K., Zuo, W., and Zhang, L. (2019, January 16\u201320). Toward Convolutional Blind Denoising of Real Photographs. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00181"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7317","DOI":"10.1109\/TGRS.2019.2912909","article-title":"Hybrid noise removal in hyperspectral imagery with a spatial-spectral gradient network","volume":"57","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","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_28","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_29","doi-asserted-by":"crossref","unstructured":"Venkatakrishnan, S.V., Bouman, C.A., and Wohlberg, B. (2013, January 3\u20135). Plug-and-Play priors for model based reconstruction. Proceedings of the 2013 IEEE Global Conference on Signal and Information Processing, Austin, TX, USA.","DOI":"10.1109\/GlobalSIP.2013.6737048"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TCI.2016.2629286","article-title":"Plug-and-play ADMM for image restoration: Fixed-point convergence and applications","volume":"3","author":"Chan","year":"2016","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1137\/16M1102884","article-title":"The little engine that could: Regularization by denoising (RED)","volume":"10","author":"Romano","year":"2017","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1109\/JSTARS.2020.2979801","article-title":"Hyperspectral Mixed Noise Removal By \u21131-Norm-Based Subspace Representation","volume":"13","author":"Zhuang","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3373","DOI":"10.1109\/TGRS.2014.2375320","article-title":"A convex formulation for hyperspectral image superresolution via subspace-based regularization","volume":"53","author":"Simoes","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/TGRS.2011.2162649","article-title":"Spectral-Spatial Hyperspectral Image Segmentation Using Subspace Multinomial Logistic Regression and Markov Random Fields","volume":"50","author":"Li","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/LGRS.2014.2341044","article-title":"Subspace-Based Support Vector Machines for Hyperspectral Image Classification","volume":"12","author":"Gao","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9858","DOI":"10.1109\/TGRS.2019.2929776","article-title":"Regularization Parameter Selection in Minimum Volume Hyperspectral Unmixing","volume":"57","author":"Zhuang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","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."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1109\/TIP.2010.2076294","article-title":"An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems","volume":"20","author":"Afonso","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1109\/TIP.2010.2047910","article-title":"Fast image recovery using variable splitting and constrained optimization","volume":"19","author":"Afonso","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","article-title":"On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators","volume":"55","author":"Eckstein","year":"1992","journal-title":"Math. Program."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Combettes, P., and Patric, J.C. (2011). Proximal splitting methods in signal processing. Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer.","DOI":"10.1007\/978-1-4419-9569-8_10"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.1109\/TIP.2010.2053941","article-title":"Restoration of Poissonian images using alternating direction optimization","volume":"19","author":"Figueiredo","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TIP.2018.2869727","article-title":"A convergent image fusion algorithm using scene-adapted Gaussian-mixture-based denoising","volume":"28","author":"Teodoro","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/TNNLS.2020.2980398","article-title":"Regularizing hyperspectral and multispectral image fusion by CNN denoiser","volume":"32","author":"Dian","year":"2021","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1109\/JSTARS.2012.2227245","article-title":"A comparative study on linear regression-based noise estimation for hyperspectral imagery","volume":"6","author":"Gao","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_46","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_47","doi-asserted-by":"crossref","first-page":"5800","DOI":"10.1109\/TIP.2015.2487862","article-title":"Collaborative sparse regression using spatially correlated supports-application to hyperspectral unmixing","volume":"24","author":"Altmann","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_48","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_49","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_50","doi-asserted-by":"crossref","first-page":"7018","DOI":"10.1109\/TGRS.2016.2594080","article-title":"Remote sensing image stripe noise removal: From image decomposition perspective","volume":"54","author":"Chang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Golub, G.H., and Reinsch, C. (1971). Singular value decomposition and least squares solutions. Linear Algebra, Springer.","DOI":"10.1007\/978-3-662-39778-7_10"},{"key":"ref_52","first-page":"2080","article-title":"Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization","volume":"58","author":"Wright","year":"2009","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TGRS.2005.844293","article-title":"Vertex component analysis: A fast algorithm to unmix hyperspectral data","volume":"43","author":"Nascimento","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J.M., and Figueiredo, M. (2010, January 14\u201316). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. Proceedings of the 2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Reykjav\u00edk, Iceland.","DOI":"10.1109\/WHISPERS.2010.5594963"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/20\/4098\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:12:42Z","timestamp":1760166762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/20\/4098"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,13]]},"references-count":54,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["rs13204098"],"URL":"https:\/\/doi.org\/10.3390\/rs13204098","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,13]]}}}