{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:58Z","timestamp":1760240818227,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2019,9,29]],"date-time":"2019-09-29T00:00:00Z","timestamp":1569715200000},"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":["61771391,61371152"],"award-info":[{"award-number":["61771391,61371152"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Technology and Innovation Commission of Shenzhen Municipality","award":["JCYJ20170815162956949, JCYJ20180306171146740"],"award-info":[{"award-number":["JCYJ20170815162956949, JCYJ20180306171146740"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A hyperspectral image (HSI) contains abundant spatial and spectral information, but it is always corrupted by various noises, especially Gaussian noise. Global correlation (GC) across spectral domain and nonlocal self-similarity (NSS) across spatial domain are two important characteristics for an HSI. To keep the integrity of the global structure and improve the details of the restored HSI, we propose a global and nonlocal weighted tensor norm minimum denoising method which jointly utilizes GC and NSS. The weighted multilinear rank is utilized to depict the GC information. To preserve structural information with NSS, a patch-group-based low-rank-tensor-approximation (LRTA) model is designed. The LRTA makes use of Tucker decompositions of 4D patches, which are composed of a similar 3D patch group of HSI. The alternating direction method of multipliers (ADMM) is adapted to solve the proposed models. Experimental results show that the proposed algorithm can preserve the structural information and outperforms several state-of-the-art denoising methods.<\/jats:p>","DOI":"10.3390\/rs11192281","type":"journal-article","created":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T05:58:33Z","timestamp":1569823113000},"page":"2281","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Hyperspectral Image Denoising Using Global Weighted Tensor Norm Minimum and Nonlocal Low-Rank Approximation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1668-4318","authenticated-orcid":false,"given":"Xiangyang","family":"Kong","sequence":"first","affiliation":[{"name":"Research &amp; Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China"},{"name":"Ministry 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":"Research &amp; Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China"}]},{"given":"Jize","family":"Xue","sequence":"additional","affiliation":[{"name":"Research &amp; Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China"}]},{"given":"Jonathan Cheung-Wai","family":"Chan","sequence":"additional","affiliation":[{"name":"Department of Electronics and Informatics, Vrije Universiteit Brussel, 1050 Brussel, Belgium"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rasti, B., Scheunders, P., Ghamisi, P., Licciardi, G., and Chanussot, J. (2018). Noise Reduction in Hyperspectral Imagery: Overview and Application. Remote Sens., 10.","DOI":"10.3390\/rs10030482"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3325","DOI":"10.1109\/TGRS.2014.2374218","article-title":"Object detection in optical remote sensing images based on weakly supervised learning and high-level feature learning","volume":"53","author":"Han","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/TGRS.2011.2162339","article-title":"On Combining Multiple Features for Hyperspectral Remote Sensing Image Classification","volume":"50","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3707","DOI":"10.1109\/TGRS.2013.2274875","article-title":"Hyperspectral image classification by nonlocal joint collaborative representation with a locally adaptive dictionary","volume":"52","author":"Li","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7738","DOI":"10.1109\/TGRS.2014.2318058","article-title":"Spectral\u2013spatial hyperspectral image classification via multiscale adaptive sparse representation","volume":"52","author":"Fang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1109\/LGRS.2011.2107726","article-title":"Unsupervised Classification of Spectropolarimetric Data by Region-Based Evidence Fusion","volume":"8","author":"Zhao","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6884","DOI":"10.1109\/TGRS.2018.2845450","article-title":"Tensor-based classification models for hyperspectral data analysis","volume":"56","author":"Makantasis","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","first-page":"4085","article-title":"Semisupervised hyperspectral image segmentation using multinomial logistic regression with active learning","volume":"48","author":"Li","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3823","DOI":"10.1109\/TGRS.2017.2681721","article-title":"Joint Hyperspectral Super-Resolution and Unmixing with Interactive Feedback","volume":"55","author":"Yi","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1109\/TGRS.2015.2489218","article-title":"Coupled Sparse Denoising and Unmixing with Low Rank Constraint for Hyper-spectral Image","volume":"54","author":"Yang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","first-page":"498","article-title":"Data-driven quadratic correlation filter using sparse coding for infrared targets detection","volume":"33","author":"Gao","year":"2014","journal-title":"J. Infrared Millim. Waves"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.ins.2019.06.012","article-title":"Hyper-Laplacian Regularized Nonlocal Low-rank Matrix Recovery for Hyperspectral Image Compressive Sensing Reconstruction","volume":"501","author":"Xue","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49955","DOI":"10.1109\/ACCESS.2018.2868731","article-title":"Total Variation and Rank-1 Constraint RPCA for Background Subtraction","volume":"6","author":"Xue","year":"2018","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Yi, C., Zhao, Y.Q., and Chan, J.C.W. (2019). Spectral super-resolution for multispectral image based on spectral improvement strategy and spatial preservation strategy. IEEE Trans. Geosci. Remote Sens., 1\u201315.","DOI":"10.1109\/IGARSS.2019.8898630"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1109\/TIT.2013.2248875","article-title":"Worst-Case Additive Noise in Wireless Networks","volume":"59","author":"Shomorony","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","first-page":"294","article-title":"Tensor decompositions and applications","volume":"66","author":"Kolda","year":"2005","journal-title":"J. SIAM Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1137\/S0895479896305696","article-title":"A multilinear singular value decomposition","volume":"21","author":"Lathauwer","year":"2000","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_18","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_19","unstructured":"Buades, A., Coll, B., and Morel, J.-M. (2005, January 20\u201325). A non-local algorithm for image denoising. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA."},{"key":"ref_20","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 Process."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1109\/LGRS.2017.2764059","article-title":"Automatic Hyperspectral Image Restoration Using Sparse and Low-Rank Modeling","volume":"14","author":"Rasti","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","unstructured":"Xue, J., Zhao, Y., Liao, W., and Chan, J.C.-W. (2019). Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction. Remote Sens., 11.","DOI":"10.3390\/rs11020193"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/LGRS.2008.915736","article-title":"Denoising and dimensionality reduction using multilinear tools for hyperspectral images","volume":"5","author":"Renard","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1109\/TGRS.2017.2771155","article-title":"Joint Spatial and Spectral Low-Rank Regularization for Hyperspectral Image Denoising","volume":"56","author":"Xue","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","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_28","unstructured":"Sena, M.M., Trevisan, M.G., and Poppi, R.J. (2005). Parallel factor analysis. Practical Three-Way Calibration, Elsevier."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ins.2019.06.061","article-title":"Nonconvex tensor rank minimization and its applications to tensor recovery","volume":"503","author":"Xue","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_30","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, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.187"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Peng, Y., Meng, D., Xu, Z., Gao, C., Yang, Y., and Zhang, B. (2014, January 23\u201328). Decomposable Nonlocal Tensor Dictionary Learning for Multispectral Image Denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.377"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.laa.2006.08.023","article-title":"A randomized algorithm for a tensor-based generalization of the singular value decomposition","volume":"420","author":"Drineas","year":"2007","journal-title":"Linear Algebra Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1137\/040616024","article-title":"A review of image denoising algorithms, with a new one","volume":"4","author":"Buades","year":"2005","journal-title":"Multiscale Model. Simul."},{"key":"ref_34","unstructured":"Yan, L., Fang, H., Zhong, S., Zhang, Z., and Chang, Y. (2017). Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.cam.2017.01.022","article-title":"A patch-based low-rank tensor approximation model for multiframe image denoising","volume":"329","author":"Hao","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5174","DOI":"10.1109\/TGRS.2019.2897316","article-title":"Nonlocal Low-Rank Regularized Tensor Decomposition for Hyperspectral Image Denoising","volume":"57","author":"Xue","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Gu, S., Zhang, L., Zuo, W., and Feng, X. (2014, January 23\u201328). Weighted Nuclear Norm Minimization with Application to Image Denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.366"},{"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":"2011","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Fu, Y., Wang, R., Jin, Y., and Zhang, H. (2015, January 20\u201322). Fast image fusion based on alternating direction algorithms. Proceedings of the 12th International Conference on Signal Processing, Alsace, France.","DOI":"10.1109\/ICOSP.2014.7015096"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Dong, W., Li, G., Shi, G., Li, X., and Ma, Y. (2015, January 7\u201313). Low-Rank Tensor Approximation with Laplacian Scale Mixture Modeling for Multiframe Image Denoising. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Santiago, Chile.","DOI":"10.1109\/ICCV.2015.58"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00521-015-2050-5","article-title":"Nonlocal image denoising via adaptive tensor nuclear norm minimization","volume":"29","author":"Zhang","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/TNNLS.2016.2608834","article-title":"Connections Between Nuclear Norm and Frobenius Norm Based Representations","volume":"29","author":"Peng","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5076","DOI":"10.1109\/TIP.2018.2848470","article-title":"Structured AutoEncoders for Subspace Clustering","volume":"27","author":"Peng","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1109\/TCYB.2016.2536752","article-title":"Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering","volume":"47","author":"Peng","year":"2012","journal-title":"IEEE Trans. Cybern."},{"key":"ref_45","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 Process."},{"key":"ref_46","unstructured":"Wald, L. (2002). Data Fusion: Definitions and Architectures. Fusion of Images of Different Spatial Resolutions, Presses de l\u2019Ecole, Ecole des Mines de Paris."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2378","DOI":"10.1109\/TIP.2011.2109730","article-title":"Fsim: A feature similarity index for image quality assessment","volume":"20","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Du, P., Chen, Y., Fang, T., and Tang, H. (2005). Error analysis and improvements of spectral angle mapper (SAM) model. MIPPR 2005: SAR and Multispectral Image Processing, International Society for Optics and Photonics.","DOI":"10.1117\/12.654850"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Yang, J., Zhao, Y., Yi, C., and Chan, J.C.W. (2017). No-Reference Hyperspectral Image Quality Assessment via Quality-Sensitive Features Learning. Remote Sens., 9.","DOI":"10.3390\/rs9040305"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/19\/2281\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:26:01Z","timestamp":1760189161000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/19\/2281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,29]]},"references-count":49,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["rs11192281"],"URL":"https:\/\/doi.org\/10.3390\/rs11192281","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,9,29]]}}}