{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T22:40:52Z","timestamp":1788302452149,"version":"build-2803163510"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T00:00:00Z","timestamp":1468195200000},"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":["61275098"],"award-info":[{"award-number":["61275098"]}],"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":["61503288"],"award-info":[{"award-number":["61503288"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ph.D. Programs Foundation of Ministry of Education of China","award":["20120142110088"],"award-info":[{"award-number":["20120142110088"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2015M570665"],"award-info":[{"award-number":["2015M570665"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Recently, sparse unmixing (SU) of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM), which ignores the possible nonlinear effects (i.e., nonlinearity). In this paper, we propose a new method named robust collaborative sparse regression (RCSR) based on the robust LMM (rLMM) for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM) is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/rs8070588","type":"journal-article","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T09:47:19Z","timestamp":1468230439000},"page":"588","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Hyperspectral Unmixing with Robust Collaborative Sparse Regression"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1724-316X","authenticated-orcid":false,"given":"Chang","family":"Li","sequence":"first","affiliation":[{"name":"School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Ma","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoguang","family":"Mei","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengyin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3264-3265","authenticated-orcid":false,"given":"Jiayi","family":"Ma","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2832","DOI":"10.1109\/TGRS.2014.2365676","article-title":"Local-manifold-learning-based graph construction for semisupervised hyperspectral image classification","volume":"53","author":"Ma","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6469","DOI":"10.1109\/TGRS.2015.2441954","article-title":"Robust feature matching for remote sensing image registration via locally linear transforming","volume":"53","author":"Ma","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1604","DOI":"10.1364\/JOSAA.32.001604","article-title":"Hyperspectral image denoising using the robust low-rank tensor recovery","volume":"32","author":"Li","year":"2015","journal-title":"JOSA A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/LGRS.2015.2503142","article-title":"Unsupervised multilayer feature learning for satellite image scene classification","volume":"13","author":"Li","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2813","DOI":"10.1364\/AO.55.002813","article-title":"Infrared spectrum blind deconvolution algorithm via learned dictionaries and sparse representation","volume":"55","author":"Liu","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1109\/TGRS.2014.2336858","article-title":"Constrained least squares algorithms for nonlinear unmixing of hyperspectral imagery","volume":"53","author":"Pu","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1974","DOI":"10.3390\/rs5041974","article-title":"Using Physically-Modeled Synthetic data to assess hyperspectral unmixing approaches","volume":"5","author":"Stites","year":"2013","journal-title":"Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"532","DOI":"10.3390\/rs4020532","article-title":"Two linear unmixing algorithms to recognize targets using supervised classification and orthogonal rotation in airborne hyperspectral images","volume":"4","author":"Averbuch","year":"2012","journal-title":"Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1007\/s11760-012-0392-3","article-title":"Blind nonlinear hyperspectral unmixing based on constrained kernel nonnegative matrix factorization","volume":"8","author":"Li","year":"2014","journal-title":"Signal Image Video Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1109\/TGRS.2015.2459763","article-title":"Reweighted sparse regression for hyperspectral unmixing","volume":"54","author":"Zheng","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1109\/JSTARS.2015.2403254","article-title":"Equivalent-sparse unmixing through spatial and spectral constrained endmember selection from an image-derived spectral library","volume":"8","author":"Mei","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"187","DOI":"10.3390\/rs8030187","article-title":"L0-norm sparse hyperspectral unmixing using arctan smoothing","volume":"8","author":"Gazor","year":"2016","journal-title":"Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/TIP.2015.2467217","article-title":"Non-rigid point set registration by preserving global and local structures","volume":"25","author":"Ma","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J.M., and Figueiredo, M.A. (2010, January 14\u201316). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. Proceedings of the IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, Reykjavik, Iceland.","DOI":"10.1109\/WHISPERS.2010.5594963"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4484","DOI":"10.1109\/TGRS.2012.2191590","article-title":"Total variation spatial regularization for sparse hyperspectral unmixing","volume":"50","author":"Iordache","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2014","DOI":"10.1109\/TGRS.2010.2098413","article-title":"Sparse unmixing of hyperspectral data","volume":"49","author":"Iordache","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3256","DOI":"10.1109\/TGRS.2013.2272076","article-title":"Subspace matching pursuit for sparse unmixing of hyperspectral data","volume":"52","author":"Shi","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1109\/TGRS.2013.2240001","article-title":"Collaborative sparse regression for hyperspectral unmixing","volume":"52","author":"Iordache","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1109\/JSTARS.2014.2320576","article-title":"A review of nonlinear hyperspectral unmixing methods","volume":"7","author":"Heylen","year":"2014","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1109\/LGRS.2016.2555341","article-title":"GBM-based unmixing of hyperspectral data using bound projected optimal gradient method","volume":"13","author":"Li","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MSP.2013.2279274","article-title":"Nonlinear unmixing of hyperspectral images: Models and algorithms","volume":"31","author":"Dobigeon","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3039","DOI":"10.1029\/JB086iB04p03039","article-title":"Bidirectional reflectance spectroscopy: 1. Theory","volume":"86","author":"Hapke","year":"1981","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2951","DOI":"10.1080\/01431160802558659","article-title":"Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated-forest hyperspectral data","volume":"30","author":"Fan","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4153","DOI":"10.1109\/TGRS.2010.2098414","article-title":"Nonlinear unmixing of hyperspectral images using a generalized bilinear model","volume":"49","author":"Halimi","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4404","DOI":"10.1109\/TGRS.2013.2281981","article-title":"Abundance estimation for bilinear mixture models via joint sparse and low-rank representation","volume":"52","author":"Qu","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TGRS.2015.2453915","article-title":"A multilinear mixing model for nonlinear spectral unmixing","volume":"54","author":"Heylen","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4163","DOI":"10.1109\/TGRS.2011.2160950","article-title":"Pixel unmixing in hyperspectral data by means of neural networks","volume":"49","author":"Licciardi","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TSP.2012.2222390","article-title":"Nonlinear unmixing of hyperspectral data based on a linear-mixture\/ nonlinear-fluctuation model","volume":"61","author":"Chen","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2654","DOI":"10.1109\/TGRS.2013.2264392","article-title":"Nonlinear estimation of material abundances in hyperspectral images with L1-norm spatial regularization","volume":"52","author":"Chen","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3968","DOI":"10.1109\/TIP.2014.2314022","article-title":"Unsupervised post-nonlinear unmixing of hyperspectral images using a Hamiltonian Monte Carlo algorithm","volume":"23","author":"Altmann","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4810","DOI":"10.1109\/TIP.2015.2468177","article-title":"Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization","volume":"24","author":"Dobigeon","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_32","unstructured":"Lin, Z., Chen, M., and Ma, Y. (2010). The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Guo, Z., Wittman, T., and Osher, S. (2009). L1 unmixing and its application to hyperspectral image enhancement. Proc. SPIE.","DOI":"10.1117\/12.818245"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/TIT.2009.2034789","article-title":"Average case analysis of multichannel sparse recovery using convex relaxation","volume":"56","author":"Eldar","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5510","DOI":"10.1109\/TIP.2014.2362056","article-title":"Blind and fully constrained unmixing of hyperspectral images","volume":"23","author":"Ammanouil","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4692","DOI":"10.1109\/TSP.2008.927802","article-title":"Reduce and boost: Recovering arbitrary sets of jointly sparse vectors","volume":"56","author":"Mishali","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","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_38","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.inffus.2016.02.001","article-title":"Infrared and visible image fusion via gradient transfer and total variation minimization","volume":"31","author":"Ma","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","article-title":"Sparse reconstruction by separable approximation","volume":"57","author":"Wright","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_40","unstructured":"Zhang, Y. (2010). IPAM Workshop: Numerical Methods for Continuous Optimization, UCLA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1109\/TMM.2014.2311320","article-title":"Noise robust face hallucination viaLocality-constrained representation","volume":"16","author":"Jiang","year":"2014","journal-title":"IEEE Trans. Multimedia"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/7\/588\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:51Z","timestamp":1760210751000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/7\/588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,11]]},"references-count":41,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["rs8070588"],"URL":"https:\/\/doi.org\/10.3390\/rs8070588","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,11]]}}}