{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T16:35:25Z","timestamp":1776357325479,"version":"3.51.2"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T00:00:00Z","timestamp":1646870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61922013"],"award-info":[{"award-number":["61922013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The low-rank and sparse decomposition model has been favored by the majority of hyperspectral image anomaly detection personnel, especially the robust principal component analysis(RPCA) model, over recent years. However, in the RPCA model, \u21130 operator minimization is an NP-hard problem, which is applicable in both low-rank and sparse items. A general approach is to relax the \u21130 operator to \u21131-norm in the traditional RPCA model, so as to approximately transform it to the convex optimization field. However, the solution obtained by convex optimization approximation often brings the problem of excessive punishment and inaccuracy. On this basis, we propose a non-convex regularized approximation model based on low-rank and sparse matrix decomposition (LRSNCR), which is closer to the original problem than RPCA. The WNNM and Capped \u21132,1-norm are used to replace the low-rank item and sparse item of the matrix, respectively. Based on the proposed model, an effective optimization algorithm is then given. Finally, the experimental results on four real hyperspectral image datasets show that the proposed LRSNCR has better detection performance.<\/jats:p>","DOI":"10.3390\/rs14061343","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T20:19:10Z","timestamp":1646943550000},"page":"1343","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Hyperspectral Anomaly Detection Based on Improved RPCA with Non-Convex Regularization"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1902-821X","authenticated-orcid":false,"given":"Wei","family":"Yao","sequence":"first","affiliation":[{"name":"School of Automation, Beijing Information Science and Technology University, Beijing 100192, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9823-0565","authenticated-orcid":false,"given":"Lu","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Information Science and Technology University, Beijing 100192, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1389-3317","authenticated-orcid":false,"given":"Hongyu","family":"Ni","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Information Science and Technology University, Beijing 100192, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7015-7335","authenticated-orcid":false,"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5243-7189","authenticated-orcid":false,"given":"Ran","family":"Tao","sequence":"additional","affiliation":[{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,10]]},"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":"1373","DOI":"10.1109\/LGRS.2019.2948960","article-title":"Random Subspace Ensemble With Enhanced Feature for Hyperspectral Image Classification","volume":"17","author":"Jiang","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1109\/TGRS.2014.2343955","article-title":"Collaborative Representation for Hyperspectral Anomaly Detection","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8615","DOI":"10.1109\/TGRS.2020.3041157","article-title":"Deep Autoencoders With Multitask Learning for Bilinear Hyperspectral Unmixing","volume":"59","author":"Su","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhu, X., Cao, L., Wang, S., Gao, L., and Zhong, Y. (2021). Anomaly Detection in Airborne Fourier Transform Thermal Infrared Spectrometer Images Based on Emissivity and a Segmented Low-Rank Prior. Remote Sens., 13.","DOI":"10.3390\/rs13040754"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MGRS.2019.2902525","article-title":"Hypersectral Imaging for Military and Security Applications: Combining Myriad Processing and Sensing Techniques","volume":"7","author":"Shimoni","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_7","first-page":"102461","article-title":"Hyperspectral target detection based on transform domain adaptive constrained energy minimization","volume":"103","author":"Zhao","year":"2021","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_8","unstructured":"Liu, J., Hou, Z., Li, W., Tao, R., Orlando, D., and Li, H. (2021). Multipixel Anomaly Detection With Unknown Patterns for Hyperspectral Imagery. IEEE Trans. Neural Netw. Learn. Syst., 1\u201311."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"112305","DOI":"10.1007\/s11432-020-2915-2","article-title":"Collaborative Representation with Background Purification and Saliency Weight for Hyperspectral Anomaly Detection","volume":"65","author":"Hou","year":"2022","journal-title":"Sci. China Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1109\/JSTARS.2014.2311995","article-title":"A Robust Nonlinear Hyperspectral Anomaly Detection Approach","volume":"7","author":"Zhao","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1109\/TGRS.2010.2081677","article-title":"Random-Selection-Based Anomaly Detector for Hyperspectral Imagery","volume":"49","author":"Du","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1109\/LGRS.2020.2998576","article-title":"A Spectral\u2013Spatial Method Based on Fractional Fourier Transform and Collaborative Representation for Hyperspectral Anomaly Detection","volume":"18","author":"Zhao","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1109\/29.60107","article-title":"Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution","volume":"38","author":"Reed","year":"1990","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5982","DOI":"10.1109\/JSTARS.2020.3028372","article-title":"A Spectral\u2013Spatial Anomaly Target Detection Method Based on Fractional Fourier Transform and Saliency Weighted Collaborative Representation for Hyperspectral Images","volume":"13","author":"Zhao","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_15","first-page":"83902J","article-title":"Comparative evaluation of hyperspectral anomaly detectors in different types of background","volume":"8390","author":"Borghys","year":"2012","journal-title":"Int. Soc. Opt. Photonics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2351","DOI":"10.1109\/JSTARS.2014.2302446","article-title":"Weighted-RXD and Linear Filter-Based RXD: Improving Background Statistics Estimation for Anomaly Detection in Hyperspectral Imagery","volume":"7","author":"Guo","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/TGRS.2004.841487","article-title":"Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery","volume":"43","author":"Kwon","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/LGRS.2010.2098842","article-title":"Anomaly Detection in Hyperspectral Images Based on an Adaptive Support Vector Method","volume":"8","author":"Khazai","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1109\/LGRS.2010.2090337","article-title":"Hyperspectral Anomaly Detection With Kurtosis-Driven Local Covariance Matrix Corruption Mitigation","volume":"8","author":"Matteoli","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Du, L., Wu, Z., Xu, Y., Liu, W., and Wei, Z. (2016, January 10\u201315). Kernel low-rank representation for hyperspectral image classification. Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China.","DOI":"10.1109\/IGARSS.2016.7729118"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4363","DOI":"10.1109\/TCYB.2020.2968750","article-title":"Low-Rank and Sparse Decomposition With Mixture of Gaussian for Hyperspectral Anomaly Detection","volume":"51","author":"Li","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_22","unstructured":"Zhou, T., and Tao, D. (July, January 28). GoDec: Randomized Lowrank & Sparse Matrix Decomposition in Noisy Case. Proceedings of the International Conference on Machine Learning, Bellevue, WA, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1109\/TGRS.2015.2479299","article-title":"A Low-Rank and Sparse Matrix Decomposition-Based Mahalanobis Distance Method for Hyperspectral Anomaly Detection","volume":"54","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"5801","DOI":"10.1109\/TGRS.2016.2572400","article-title":"A Tensor Decomposition-Based Anomaly Detection Algorithm for Hyperspectral Image","volume":"54","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","first-page":"1","article-title":"Robust Principal Component Analysis?","volume":"58","author":"Li","year":"2011","journal-title":"J. ACM"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"083641","DOI":"10.1117\/1.JRS.8.083641","article-title":"Low-rank and sparse matrix decomposition-based anomaly detection for hyperspectral imagery","volume":"8","author":"Sun","year":"2014","journal-title":"J. Appl. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties","volume":"96","author":"Li","year":"2001","journal-title":"Publ. Am. Stat. Assoc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1214\/09-AOS729","article-title":"Nearly unbiased variable selection under minimax concave penalty","volume":"38","author":"Zhang","year":"2010","journal-title":"Ann. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhao, X., Li, W., Zhang, M., Tao, R., and Ma, P. (2020). Adaptive Iterated Shrinkage Thresholding-Based Lp-Norm Sparse Representation for Hyperspectral Imagery Target Detection. Remote Sens., 12.","DOI":"10.3390\/rs12233991"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","article-title":"Enhancing Sparsity by Reweighted \u21131 Minimization","volume":"14","author":"Wakin","year":"2008","journal-title":"J. Fourier Anal. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TMI.2008.927346","article-title":"Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic \u21130-Minimization","volume":"28","author":"Trzasko","year":"2009","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_33","unstructured":"Gong, P., Ye, J., and Zhang, C. (2012). Multi-stage multi-task feature learning. Adv. Neural Inf. Process. Syst., 25, Available online: https:\/\/proceedings.neurips.cc\/paper\/2012\/hash\/2ab56412b1163ee131e1246da0955bd1-Abstract.html."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"115910","DOI":"10.1016\/j.eswa.2021.115910","article-title":"A predictive hybrid reduced order model based on proper orthogonal decomposition combined with deep learning architectures","volume":"187","author":"Carro","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"114924","DOI":"10.1016\/j.eswa.2021.114924","article-title":"Model-free short-term fluid dynamics estimator with a deep 3D-convolutional neural network","volume":"177","author":"Carro","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1137\/070697835","article-title":"Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization","volume":"52","author":"Recht","year":"2010","journal-title":"SIAM Rev."},{"key":"ref_37","first-page":"8123533","article-title":"Generalized Singular Value Thresholding","volume":"29","author":"Lu","year":"2014","journal-title":"Comput. Sci."},{"key":"ref_38","unstructured":"Fazel, M. (2002). Matrix Rank Minimization with Applications. [Ph.D. Thesis, Stanford University]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11263-016-0930-5","article-title":"Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision","volume":"121","author":"Gu","year":"2017","journal-title":"Int. J. Comput. Vis."},{"key":"ref_40","unstructured":"Gong, P., Zhang, C., Lu, Z., Huang, J.Z., and Ye, J. (2013, January 17\u201319). A General Iterative Shrinkage and Thresholding Algorithm for Non-Convex Regularized Optimization Problems. Proceedings of the 30th International Conference on International Conference on Machine Learning, Atlanta, GA, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/TIP.2015.2511584","article-title":"Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm","volume":"25","author":"Lu","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_42","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_43","first-page":"619","article-title":"Understanding the convergence of the alternating direction method of multipliers: Theoretical and computational perspectives","volume":"11","author":"Eckstein","year":"2015","journal-title":"Pac. J. Optim."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.neucom.2020.01.103","article-title":"Spatial-Spectral Weighted Nuclear Norm Minimization for Hyperspectral Image Denoising","volume":"399","author":"Huang","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5600","DOI":"10.1109\/TGRS.2017.2710145","article-title":"Hyperspectral Anomaly Detection With Attribute and Edge-Preserving Filters","volume":"55","author":"Kang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1109\/TNNLS.2020.3038659","article-title":"Prior-Based Tensor Approximation for Anomaly Detection in Hyperspectral Imagery","volume":"33","author":"Li","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_47","first-page":"839028","article-title":"SpecTIR hyperspectral airborne Rochester experiment data collection campaign","volume":"8390","author":"Herweg","year":"2012","journal-title":"Spie Def. Secur. Sens."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3208","DOI":"10.1109\/TGRS.2017.2664658","article-title":"Hyperspectral Anomaly Detection via a Sparsity Score Estimation Framework","volume":"55","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_49","first-page":"5507312","article-title":"Hyperspectral Change Detection Based on Multiple Morphological Profiles","volume":"60","author":"Hou","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/6\/1343\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:34:09Z","timestamp":1760135649000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/6\/1343"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,10]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["rs14061343"],"URL":"https:\/\/doi.org\/10.3390\/rs14061343","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,10]]}}}