{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T11:51:25Z","timestamp":1768737085966,"version":"3.49.0"},"reference-count":79,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T00:00:00Z","timestamp":1708560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hong Kong Innovation and Technology Commission","award":["11204821"],"award-info":[{"award-number":["11204821"]}]},{"name":"Hong Kong Innovation and Technology Commission","award":["9610460"],"award-info":[{"award-number":["9610460"]}]},{"name":"Hong Kong Research Grants Council","award":["11204821"],"award-info":[{"award-number":["11204821"]}]},{"name":"Hong Kong Research Grants Council","award":["9610460"],"award-info":[{"award-number":["9610460"]}]},{"name":"City University of Hong Kong","award":["11204821"],"award-info":[{"award-number":["11204821"]}]},{"name":"City University of Hong Kong","award":["9610460"],"award-info":[{"award-number":["9610460"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Hyperspectral imaging captures detailed spectral data for remote sensing. However, due to the limited spatial resolution of hyperspectral sensors, each pixel of a hyperspectral image (HSI) may contain information from multiple materials. Although the hyperspectral unmixing (HU) process involves estimating endmembers, identifying pure spectral components, and estimating pixel abundances, existing algorithms mostly focus on just one or two tasks. Blind source separation (BSS) based on nonnegative matrix factorization (NMF) algorithms identify endmembers and their abundances at each pixel of HSI simultaneously. Although they perform well, the factorization results are unstable, require high computational costs, and are difficult to interpret from the original HSI. CUR matrix decomposition selects specific columns and rows from a dataset to represent it as a product of three small submatrices, resulting in interpretable low-rank factorization. In this paper, we propose a new blind HU framework based on CUR factorization called CUR-HU that performs the entire HU process by exploiting the low-rank structure of given HSIs. CUR-HU incorporates several techniques to perform the HU process with a performance comparable to state-of-the-art methods but with higher computational efficiency. We adopt a deterministic sampling method to select the most informative pixels and spectrum components in HSIs. We use an incremental QR decomposition method to reduce computation complexity and estimate the number of endmembers. Various experiments on synthetic and real HSIs are conducted to evaluate the performance of CUR-HU. CUR-HU performs comparably to state-of-the-art methods for estimating the number of endmembers and abundance maps, but it outperforms other methods for estimating the endmembers and the computational efficiency. It has a 9.4 to 249.5 times speedup over different methods for different real HSIs.<\/jats:p>","DOI":"10.3390\/rs16050766","type":"journal-article","created":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T11:28:47Z","timestamp":1708601327000},"page":"766","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Efficient Blind Hyperspectral Unmixing Framework Based on CUR Decomposition (CUR-HU)"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8285-3516","authenticated-orcid":false,"given":"Muhammad A. A.","family":"Abdelgawad","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis, City University of Hong Kong, Hong Kong"}]},{"given":"Ray C. C.","family":"Cheung","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis, City University of Hong Kong, Hong Kong"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9661-3095","authenticated-orcid":false,"given":"Hong","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis, City University of Hong Kong, Hong Kong"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"S5","DOI":"10.1016\/j.rse.2007.12.014","article-title":"Three decades of hyperspectral remote sensing of the Earth: A personal view","volume":"113","author":"Goetz","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/MGRS.2021.3071158","article-title":"Spectral variability in hyperspectral data unmixing: A comprehensive review","volume":"9","author":"Borsoi","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/79.974727","article-title":"Spectral unmixing","volume":"19","author":"Keshava","year":"2002","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1109\/TGRS.2003.819189","article-title":"Estimation of number of spectrally distinct signal sources in hyperspectral imagery","volume":"42","author":"Chang","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/36.911111","article-title":"Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery","volume":"39","author":"Heinz","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ahmed, A.M., Duran, O., Zweiri, Y., and Smith, M. (2017). Hybrid spectral unmixing: Using artificial neural networks for linear\/non-linear switching. Remote Sens., 9.","DOI":"10.3390\/rs9080775"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Shen, X., and Bao, W. (2019). Hyperspectral endmember extraction using spatially weighted simplex strategy. Remote Sens., 11.","DOI":"10.3390\/rs11182147"},{"key":"ref_10","unstructured":"Heinz, D., Chang, C.I., and Althouse, M.L. (July, January 28). Fully constrained least-squares based linear unmixing [hyperspectral image classification]. Proceedings of the IEEE 1999 International Geoscience and Remote Sensing Symposium. IGARSS\u201999 (Cat. No. 99CH36293), Hamburg, Germany."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.isprsjprs.2016.04.008","article-title":"Blind spectral unmixing based on sparse component analysis for hyperspectral remote sensing imagery","volume":"119","author":"Zhong","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_12","unstructured":"Lee, D., and Seung, H.S. (2000). Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst., 13, Available online: https:\/\/papers.nips.cc\/paper_files\/paper\/2000\/hash\/f9d1152547c0bde01830b7e8bd60024c-Abstract.html."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2212","DOI":"10.1080\/03081087.2016.1267104","article-title":"Literature survey on low rank approximation of matrices","volume":"65","author":"Schneider","year":"2017","journal-title":"Linear Multilinear Algebra"},{"key":"ref_14","unstructured":"Zhu, F. (2017). Hyperspectral unmixing: Ground truth labeling, datasets, benchmark performances and survey. arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1073\/pnas.0803205106","article-title":"CUR matrix decompositions for improved data analysis","volume":"106","author":"Mahoney","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1137\/110852310","article-title":"Sublinear randomized algorithms for skeleton decompositions","volume":"34","author":"Chiu","year":"2013","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1109\/TGRS.2012.2213261","article-title":"Hyperspectral data geometry-based estimation of number of endmembers using p-norm-based pure pixel identification algorithm","volume":"51","author":"Ambikapathi","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Winter, M.E. (1999, January 19\u201321). N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data. Proceedings of the Imaging Spectrometry V. SPIE, Denver, CO, USA.","DOI":"10.1117\/12.366289"},{"key":"ref_21","unstructured":"Boardman, J.W. (1993, January 25\u201329). Automating spectral unmixing of AVIRIS data using convex geometry concepts. Proceedings of the JPL, Summaries of the 4th Annual JPL Airborne Geoscience Workshop, Washington, DC, USA. AVIRIS Workshop."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2804","DOI":"10.1109\/TGRS.2006.881803","article-title":"A new growing method for simplex-based endmember extraction algorithm","volume":"44","author":"Chang","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J.M. (2009, January 26\u201328). A variable splitting augmented Lagrangian approach to linear spectral unmixing. Proceedings of the 2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, Lisbon, Portugal.","DOI":"10.1109\/WHISPERS.2009.5289072"},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.isprsjprs.2018.04.008","article-title":"\u21130-based sparse hyperspectral unmixing using spectral information and a multi-objectives formulation","volume":"141","author":"Xu","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/TGRS.2014.2328336","article-title":"Sparse unmixing of hyperspectral data using spectral a priori information","volume":"53","author":"Tang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0165-1684(91)90080-3","article-title":"Blind separation of sources, Part II: Problems statement","volume":"24","author":"Comon","year":"1991","journal-title":"Signal Process."},{"key":"ref_28","unstructured":"Chen, C.H., and Zhang, X. (1999, January 22\u201324). Independent component analysis for remote sensing study. Proceedings of the Image and Signal Processing for Remote Sensing V. SPIE, Florence, Italy."},{"key":"ref_29","unstructured":"Liu, L., Wang, B., Zhang, L., and Zhang, J.Q. (2007, January 23\u201328). Decomposition of mixed pixels using Bayesian Self-Organizing Map (BSOM) neural networks. Proceedings of the 2007 IEEE International Geoscience and Remote Sensing Symposium, IEEE, Barcelona, Spain."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1109\/TGRS.2004.839806","article-title":"Does independent component analysis play a role in unmixing hyperspectral data?","volume":"43","author":"Nascimento","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","unstructured":"Nascimento, J.M.P., and Bioucas-Dias, J.M. (2007, January 23\u201328). Dependent component analysis: A hyperspectral unmixing algorithm. Proceedings of the Iberian Conference on Pattern Recognition and Image Analysis, Barcelona, Spain."},{"key":"ref_32","unstructured":"Barros, A.K. (2000). Advances in Independent Component Analysis, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.sigpro.2007.07.011","article-title":"Blind spectral unmixing by local maximization of non-Gaussianity","volume":"88","author":"Caiafa","year":"2008","journal-title":"Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.isprsjprs.2013.11.014","article-title":"Structured sparse method for hyperspectral unmixing","volume":"88","author":"Zhu","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Leplat, V., Ang, A.M., and Gillis, N. (2019, January 12\u201317). Minimum-volume rank-deficient nonnegative matrix factorizations. Proceedings of the ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8682280"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Qian, Y., Jia, S., Zhou, J., and Robles-Kelly, A. (2010, January 1\u20133). L1\/2 sparsity constrained nonnegative matrix factorization for hyperspectral unmixing. Proceedings of the 2010 International Conference on Digital Image Computing: Techniques and Applications, Sydney, Australia.","DOI":"10.1109\/DICTA.2010.82"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1109\/TGRS.2012.2213825","article-title":"Manifold regularized sparse NMF for hyperspectral unmixing","volume":"51","author":"Lu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6287","DOI":"10.1109\/TGRS.2017.2724944","article-title":"Spatial group sparsity regularized nonnegative matrix factorization for hyperspectral unmixing","volume":"55","author":"Wang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6076","DOI":"10.1109\/TGRS.2016.2580702","article-title":"Robust collaborative nonnegative matrix factorization for hyperspectral unmixing","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","first-page":"1548","article-title":"Graph regularized nonnegative matrix factorization for data representation","volume":"33","author":"Cai","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4257","DOI":"10.1109\/JSTARS.2020.3011257","article-title":"Subspace structure regularized nonnegative matrix factorization for hyperspectral unmixing","volume":"13","author":"Zhou","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2746","DOI":"10.1109\/TGRS.2013.2265322","article-title":"Double constrained NMF for hyperspectral unmixing","volume":"52","author":"Lu","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2632","DOI":"10.1109\/JSTARS.2015.2427656","article-title":"Projection-based NMF for hyperspectral unmixing","volume":"8","author":"Yuan","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_44","first-page":"102981","article-title":"Multi-stage convolutional autoencoder network for hyperspectral unmixing","volume":"113","author":"Yu","year":"2022","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4309","DOI":"10.1109\/TGRS.2018.2890633","article-title":"DAEN: Deep autoencoder networks for hyperspectral unmixing","volume":"57","author":"Su","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.isprsjprs.2021.11.008","article-title":"Deep-learning-based latent space encoding for spectral unmixing of geological materials","volume":"183","author":"Sahoo","year":"2022","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_47","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_48","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1109\/LGRS.2019.2900733","article-title":"Nonlinear unmixing of hyperspectral data via deep autoencoder networks","volume":"16","author":"Wang","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_49","first-page":"79","article-title":"Hyperspectral image processing for automatic target detection applications","volume":"14","author":"Manolakis","year":"2003","journal-title":"Linc. Lab. J."},{"key":"ref_50","first-page":"24","article-title":"Empirical automatic estimation of the number of endmembers in hyperspectral images","volume":"10","author":"Luo","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_51","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_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0024-3795(96)00301-1","article-title":"A theory of pseudoskeleton approximations","volume":"261","author":"Goreinov","year":"1997","journal-title":"Linear Algebra Its Appl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s002110050451","article-title":"Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix","volume":"83","author":"Stewart","year":"1999","journal-title":"Numer. Math."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1137\/S0097539704442684","article-title":"Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication","volume":"36","author":"Drineas","year":"2006","journal-title":"SIAM J. Comput."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"A1454","DOI":"10.1137\/140978430","article-title":"A DEIM induced CUR factorization","volume":"38","author":"Sorensen","year":"2016","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2737","DOI":"10.1137\/090766498","article-title":"Nonlinear model reduction via discrete empirical interpolation","volume":"32","author":"Chaturantabut","year":"2010","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Lehoucq, R.B., Sorensen, D.C., and Yang, C. (1998). ARPACK Users\u2019 Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898719628"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2866","DOI":"10.1016\/j.laa.2011.07.018","article-title":"Low-rank incremental methods for computing dominant singular subspaces","volume":"436","author":"Baker","year":"2012","journal-title":"Linear Algebra Its Appl."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"6752","DOI":"10.1109\/TGRS.2015.2447573","article-title":"A new fast algorithm for linearly unmixing hyperspectral images","volume":"53","author":"Guerra","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_60","first-page":"772","article-title":"Reorthogonalization and stable algorithms for updating the Gram\u2013Schmidt QR factorization","volume":"30","author":"Daniel","year":"1976","journal-title":"Math. Comput."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s00211-005-0615-4","article-title":"Rounding error analysis of the classical Gram\u2013Schmidt orthogonalization process","volume":"101","author":"Giraud","year":"2005","journal-title":"Numer. Math."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/36.3001","article-title":"A transformation for ordering multispectral data in terms of image quality with implications for noise removal","volume":"26","author":"Green","year":"1988","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1080\/01431169608948750","article-title":"Reliably estimating the noise in AVIRIS hyperspectral images","volume":"17","author":"Roger","year":"1996","journal-title":"Int. J. Remote Sens."},{"key":"ref_64","unstructured":"Boutsidis, C., and Woodruff, D.P. (June, January 31). Optimal CUR matrix decompositions. Proceedings of the the Forty-Sixth Annual ACM Symposium on Theory of Computing, New York, NY, USA."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1137\/19M128394X","article-title":"Perturbations of CUR decompositions","volume":"42","author":"Hamm","year":"2021","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1109\/LGRS.2007.895727","article-title":"Sparsity promoting iterated constrained endmember detection in hyperspectral imagery","volume":"4","author":"Zare","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0034-4257(93)90012-M","article-title":"The airborne visible\/infrared imaging spectrometer (AVIRIS)","volume":"44","author":"Vane","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_68","unstructured":"Landgrebe, D. (1998). Multispectral Data Analysis: A Signal Theory Perspective, Purdue Univiersity."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1109\/TGRS.2006.888466","article-title":"Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization","volume":"45","author":"Miao","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"11853","DOI":"10.1109\/JSTARS.2021.3126664","article-title":"Constrained nonnegative matrix factorization for blind hyperspectral unmixing incorporating endmember independence","volume":"14","author":"Ekanayake","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"3867","DOI":"10.1109\/TGRS.2007.898443","article-title":"Spectral and spatial complexity-based hyperspectral unmixing","volume":"45","author":"Jia","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"4282","DOI":"10.1109\/TGRS.2011.2144605","article-title":"Hyperspectral unmixing via l1\/2 sparsity-constrained nonnegative matrix factorization","volume":"49","author":"Qian","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1776","DOI":"10.1109\/TGRS.2016.2633279","article-title":"Matrix-vector nonnegative tensor factorization for blind unmixing of hyperspectral imagery","volume":"55","author":"Qian","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Imbiriba, T., Borsoi, R.A., and Bermudez, J.C.M. (2018, January 15\u201320). Generalized linear mixing model accounting for endmember variability. Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, BC, Canada.","DOI":"10.1109\/ICASSP.2018.8462214"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1109\/TCI.2019.2948726","article-title":"Deep generative endmember modeling: An application to unsupervised spectral unmixing","volume":"6","author":"Borsoi","year":"2019","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Chang, C.I. (2013). Hyperspectral Data Processing: Algorithm Design and Analysis, John Wiley & Sons.","DOI":"10.1002\/9781118269787"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/TSP.2015.2486746","article-title":"Hyperspectral unmixing with spectral variability using a perturbed linear mixing model","volume":"64","author":"Thouvenin","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"6712","DOI":"10.1109\/TGRS.2016.2589266","article-title":"A novel endmember bundle extraction and clustering approach for capturing spectral variability within endmember classes","volume":"54","author":"Uezato","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"3890","DOI":"10.1109\/TIP.2016.2579259","article-title":"Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability","volume":"25","author":"Drumetz","year":"2016","journal-title":"IEEE Trans. Image Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/766\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:03:16Z","timestamp":1760104996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,22]]},"references-count":79,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["rs16050766"],"URL":"https:\/\/doi.org\/10.3390\/rs16050766","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,22]]}}}