{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:21:11Z","timestamp":1762431671326,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T00:00:00Z","timestamp":1555286400000},"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":["61805181, 61705170, 61605146"],"award-info":[{"award-number":["61805181, 61705170, 61605146"]}],"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>Gaussian mixture model (GMM) has been one of the most representative models for hyperspectral unmixing while considering endmember variability. However, the GMM unmixing models only have proper smoothness and sparsity prior constraints on the abundances and thus do not take into account the possible local spatial correlation. When the pixels that lie on the boundaries of different materials or the inhomogeneous region, the abundances of the neighboring pixels do not have those prior constraints. Thus, we propose a novel GMM unmixing method based on superpixel segmentation (SS) and low-rank representation (LRR), which is called GMM-SS-LRR. we adopt the SS in the first principal component of HSI to get the homogeneous regions. Moreover, the HSI to be unmixed is partitioned into regions where the statistical property of the abundance coefficients have the underlying low-rank property. Then, to further exploit the spatial data structure, under the Bayesian framework, we use GMM to formulate the unmixing problem, and put the low-rank property into the objective function as a prior knowledge, using generalized expectation maximization to solve the objection function. Experiments on synthetic datasets and real HSIs demonstrated that the proposed GMM-SS-LRR is efficient compared with other current popular methods.<\/jats:p>","DOI":"10.3390\/rs11080911","type":"journal-article","created":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T11:15:58Z","timestamp":1555326958000},"page":"911","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Hyperspectral Unmixing with Gaussian Mixture Model and Low-Rank Representation"],"prefix":"10.3390","volume":"11","author":[{"given":"Yong","family":"Ma","sequence":"first","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Institute of Aerospace Science and Technology, Wuhan University, Whan 430079, China"}]},{"given":"Qiwen","family":"Jin","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0239-8580","authenticated-orcid":false,"given":"Xiaoguang","family":"Mei","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Institute of Aerospace Science and Technology, Wuhan University, Whan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0190-2538","authenticated-orcid":false,"given":"Xiaobing","family":"Dai","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Institute of Aerospace Science and Technology, Wuhan University, Whan 430079, China"}]},{"given":"Fan","family":"Fan","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Institute of Aerospace Science and Technology, Wuhan University, Whan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2769-4842","authenticated-orcid":false,"given":"Hao","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China"}]},{"given":"Jun","family":"Huang","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Institute of Aerospace Science and Technology, Wuhan University, Whan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,15]]},"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","doi-asserted-by":"crossref","first-page":"2783","DOI":"10.1016\/j.neucom.2017.11.052","article-title":"Robust GBM hyperspectral image unmixing with superpixel segmentation based low rank and sparse representation","volume":"275","author":"Mei","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TGRS.2018.2861992","article-title":"Hyperspectral Image Classification in the Presence of Noisy Labels","volume":"57","author":"Jiang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1392","DOI":"10.1109\/36.934072","article-title":"Hyperspectral subpixel target detection using the linear mixing model","volume":"39","author":"Manolakis","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1109\/TGRS.2018.2872850","article-title":"Centroid and Covariance Alignment-Based Domain Adaptation for Unsupervised Classification of Remote Sensing Images","volume":"57","author":"Ma","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.1109\/TGRS.2018.2828029","article-title":"SuperPCA: A Superpixelwise PCA Approach for Unsupervised Feature Extraction of Hyperspectral Imagery","volume":"56","author":"Jiang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1007\/s11263-018-1117-z","article-title":"Locality preserving matching","volume":"127","author":"Ma","year":"2019","journal-title":"Int. J. Comput. Vis."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/MGRS.2017.2762087","article-title":"Advances in hyperspectral image and signal processing: A comprehensive overview of the state of the art","volume":"5","author":"Ghamisi","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_10","unstructured":"Boardman, J.W., Kruse, F.A., and Green, R.O. (2019, April 14). Mapping Target Signatures via Partial Unmixing of AVIRIS Data. Available online: http:\/\/hdl.handle.net\/2014\/33635."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1109\/TAES.2003.1261124","article-title":"Automatic spectral target recognition in hyperspectral imagery","volume":"39","author":"Ren","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"4177","DOI":"10.1109\/TGRS.2011.2141672","article-title":"A simplex volume maximization framework for hyperspectral endmember extraction","volume":"49","author":"Chan","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2085","DOI":"10.1109\/TGRS.2004.835299","article-title":"ICE: A statistical approach to identifying endmembers in hyperspectral images","volume":"42","author":"Berman","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"3017","DOI":"10.1109\/TIP.2012.2187668","article-title":"Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery","volume":"21","author":"Altmann","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Broadwater, J., Chellappa, R., Banerjee, A., and Burlina, P. (2007, January 23\u201328). Kernel fully constrained least squares abundance estimates. Proceedings of the 2007 IEEE International Geoscience and Remote Sensing Symposium, Barcelona, Spain.","DOI":"10.1109\/IGARSS.2007.4423736"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Broadwater, J., and Banerjee, A. (2010, January 14\u201316). A generalized kernel for areal and intimate mixtures. Proceedings of the 2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Reykjavik, Iceland.","DOI":"10.1109\/WHISPERS.2010.5594962"},{"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. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/MSP.2013.2279177","article-title":"Endmember variability in hyperspectral analysis: Addressing spectral variability during spectral unmixing","volume":"31","author":"Zare","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0034-4257(98)00037-6","article-title":"Mapping chaparral in the Santa Monica Mountains using multiple endmember spectral mixture models","volume":"65","author":"Roberts","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1016\/j.pss.2007.12.007","article-title":"Analysis of OMEGA\/Mars express data hyperspectral data using a multiple-endmember linear spectral unmixing model (MELSUM): Methodology and first results","volume":"56","author":"Combe","year":"2008","journal-title":"Planet. Space Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0034-4257(00)00126-7","article-title":"A biogeophysical approach for automated SWIR unmixing of soils and vegetation","volume":"74","author":"Asner","year":"2000","journal-title":"Remote Sens. Environ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3939","DOI":"10.1080\/01431160110115960","article-title":"Spectral unmixing of vegetation, soil and dry carbon cover in arid regions: Comparing multispectral and hyperspectral observations","volume":"23","author":"Asner","year":"2002","journal-title":"Int. J. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0034-4257(03)00135-4","article-title":"Endmember selection for multiple endmember spectral mixture analysis using endmember average RMSE","volume":"87","author":"Dennison","year":"2003","journal-title":"Remote Sens. Environ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/36.841987","article-title":"Endmember bundles: A new approach to incorporating endmember variability into spectral mixture analysis","volume":"38","author":"Bateson","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/j.rse.2011.03.003","article-title":"Endmember variability in spectral mixture analysis: A review","volume":"115","author":"Somers","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1109\/LGRS.2010.2046134","article-title":"A novel approach based on fisher discriminant null space for decomposition of mixed pixels in hyperspectral imagery","volume":"7","author":"Jin","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1109\/TIP.2010.2042993","article-title":"Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery","volume":"19","author":"Eches","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_30","unstructured":"Stein, D. (2003, January 27\u201328). Application of the normal compositional model to the analysis of hyperspectral imagery. Proceedings of the 2003 IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, Greenbelt, MD, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4904","DOI":"10.1109\/TIP.2015.2471182","article-title":"Unsupervised unmixing of hyperspectral images accounting for endmember variability","volume":"24","author":"Halimi","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"7782","DOI":"10.1109\/TGRS.2014.2319337","article-title":"PSO-EM: A hyperspectral unmixing algorithm based on normal compositional model","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1994","DOI":"10.1109\/JSTARS.2014.2330347","article-title":"Spatial and spectral unmixing using the beta compositional model","volume":"7","author":"Du","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2242","DOI":"10.1109\/TIP.2018.2795744","article-title":"A Gaussian mixture model representation of endmember variability in hyperspectral unmixing","volume":"27","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4239","DOI":"10.1109\/TGRS.2011.2140119","article-title":"Enhancing hyperspectral image unmixing with spatial correlations","volume":"49","author":"Eches","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4775","DOI":"10.1109\/TGRS.2016.2551327","article-title":"Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing","volume":"54","author":"Giampouras","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2684","DOI":"10.1109\/TSP.2008.917851","article-title":"Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery","volume":"56","author":"Dobigeon","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4355","DOI":"10.1109\/TSP.2009.2025797","article-title":"Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery","volume":"57","author":"Dobigeon","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","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_40","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_41","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1093\/biomet\/80.2.267","article-title":"Maximum likelihood estimation via the ECM algorithm: A general framework","volume":"80","author":"Meng","year":"1993","journal-title":"Biometrika"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Liu, M.Y., Tuzel, O., Ramalingam, S., and Chellappa, R. (2011, January 20\u201325). Entropy rate superpixel segmentation. Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Colorado Springs, CO, USA.","DOI":"10.1109\/CVPR.2011.5995323"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"6663","DOI":"10.1109\/TGRS.2015.2445767","article-title":"Classification of hyperspectral images by exploiting spectral\u2013spatial information of superpixel via multiple kernels","volume":"53","author":"Fang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","unstructured":"Horn, R.A., Horn, R.A., and Johnson, C.R. (1990). Matrix Analysis, Cambridge University Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","article-title":"Robust recovery of subspace structures by low-rank representation","volume":"35","author":"Liu","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1023\/A:1013844811137","article-title":"A greedy EM algorithm for Gaussian mixture learning","volume":"15","author":"Vlassis","year":"2002","journal-title":"Neural Process. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.ins.2017.07.010","article-title":"Feature guided Gaussian mixture model with semi-supervised EM and local geometric constraint for retinal image registration","volume":"417","author":"Ma","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Achlioptas, D., and McSherry, F. (2005, January 27\u201330). On spectral learning of mixtures of distributions. Proceedings of the International Conference on Computational Learning Theory, Bertinoro, Italy.","DOI":"10.1007\/11503415_31"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Lange, K. (2013). The MM algorithm. Optimization, Springer.","DOI":"10.1007\/978-1-4614-5838-8"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1002\/widm.1135","article-title":"On the number of components in a Gaussian mixture model","volume":"4","author":"McLachlan","year":"2014","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1023\/A:1008940618127","article-title":"Model selection for probabilistic clustering using cross-validated likelihood","volume":"10","author":"Smyth","year":"2000","journal-title":"Stat. Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"5987","DOI":"10.1109\/TIP.2016.2618002","article-title":"A spatial compositional model for linear unmixing and endmember uncertainty estimation","volume":"25","author":"Zhou","year":"2016","journal-title":"IEEE Trans. Image Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/8\/911\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:45:28Z","timestamp":1760186728000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/8\/911"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,15]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["rs11080911"],"URL":"https:\/\/doi.org\/10.3390\/rs11080911","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,4,15]]}}}