{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T13:52:25Z","timestamp":1771336345117,"version":"3.50.1"},"reference-count":120,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Spectral unmixing of geological mixtures, such as rocks, is a challenging inversion problem because of nonlinear interactions of light with the intimately mixed minerals at a microscopic scale. The fine-scale mixing of minerals in rocks limits the sensor\u2019s ability to identify pure mineral endmembers and spectrally resolve these constituents within a given spatial resolution. In this study, we attempt to model the spectral unmixing of two rocks, namely, serpentinite and granite, by acquiring their hyperspectral images in a controlled environment, having uniform illumination, using a laboratory-based imaging spectroradiometer. The endmember spectra of each rock were identified by comparing a limited set of pure hyperspectral image pixels with the constituent minerals of the rocks based on their diagnostic spectral features. A series of spectral unmixing paradigms for explaining geological mixtures, including those ranging from simple physics-based light interaction models (linear, bilinear, and polynomial models) to classification-based models (support vector machines (SVMs) and half Siamese network (HSN)), were tested to estimate the fractional abundances of the endmembers at each pixel position of the image. The analysis of the results of the spectral unmixing algorithms using the ground truth abundance maps and actual mineralogical composition of the rock samples (estimated using X-ray diffraction (XRD) analysis) indicate a better performance of the pure pixel-guided HSN model in comparison to the linear, bilinear, polynomial, and SVM-based unmixing approaches. The HSN-based approach yielded reduced errors of abundance estimation, image reconstruction, and mineralogical composition for serpentinite and granite. With its ability to train using limited pure pixels, the half-Siamese network model has a scope for spectrally unmixing rock samples of varying mineralogical composition and grain sizes. Hence, HSN-based approaches effectively address the modelling of nonlinear mixing in geological mixtures.<\/jats:p>","DOI":"10.3390\/rs15133300","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:45:11Z","timestamp":1687913111000},"page":"3300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Modelling Spectral Unmixing of Geological Mixtures: An Experimental Study Using Rock Samples"],"prefix":"10.3390","volume":"15","author":[{"given":"Maitreya Mohan","family":"Sahoo","sequence":"first","affiliation":[{"name":"Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India"}]},{"given":"R.","family":"Kalimuthu","sequence":"additional","affiliation":[{"name":"Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India"}]},{"given":"Arun","family":"PV","sequence":"additional","affiliation":[{"name":"Indian Institute of Information Technology, Sri City 517646, India"}]},{"given":"Alok","family":"Porwal","sequence":"additional","affiliation":[{"name":"Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India"}]},{"given":"Shibu K.","family":"Mathew","sequence":"additional","affiliation":[{"name":"Udaipur Solar Observatory, Physical Research Laboratory, Udaipur 313001, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"573","DOI":"10.2113\/gsecongeo.78.4.573","article-title":"Remote sensing for exploration: An overview","volume":"78","author":"Goetz","year":"1983","journal-title":"Econ. Geol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9192","DOI":"10.1029\/JB094iB07p09192","article-title":"Thermal infrared (2.5\u201313.5 \u03bcm) spectroscopic remote sensing of igneous rock types on particulate planetary surfaces","volume":"94","author":"Salisbury","year":"1989","journal-title":"J. Geophys. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0034-4257(93)90068-9","article-title":"Spectral band selection for the characterization of salinity status of soils","volume":"43","author":"Csillag","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0034-4257(95)00171-9","article-title":"Nonlinear spectral mixing in desert vegetation","volume":"55","author":"Ray","year":"1996","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/S0034-4257(98)00097-2","article-title":"Mapping vegetation, soils, and geology in semiarid shrublands using spectral matching and mixture modeling of SWIR AVIRIS imagery","volume":"68","author":"Drake","year":"1999","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.rse.2007.01.002","article-title":"Remote sensing of water clarity in Tampa Bay","volume":"109","author":"Chen","year":"2007","journal-title":"Remote Sens. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2011","DOI":"10.1016\/j.rse.2010.04.008","article-title":"Spectral assessment of new ASTER SWIR surface reflectance data products for spectroscopic mapping of rocks and minerals","volume":"114","author":"Mars","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/978-94-007-6639-6_24","article-title":"Mineral mapping with airborne hyperspectral thermal infrared remote sensing at Cuprite, Nevada, USA","volume":"Volume 17","author":"Kuenzer","year":"2013","journal-title":"Thermal Infrared Remote Sensing: Sensors, Methods, Applications. Remote Sensing and Digital Image Processing"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.2113\/econgeo.109.5.1179","article-title":"Mapping advanced argillic alteration at Cuprite, Nevada, using imaging spectroscopy","volume":"109","author":"Swayze","year":"2014","journal-title":"Econ. Geol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.5382\/econgeo.2018.4559","article-title":"Application of imaging spectroscopy for mineral exploration in Alaska: A study over porphyry Cu deposits in the eastern Alaska Range","volume":"113","author":"Graham","year":"2018","journal-title":"Econ. Geol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9724","DOI":"10.1029\/2017WR022437","article-title":"Satellite remote sensing for water resources management: Potential for supporting sustainable development in data-poor regions","volume":"54","author":"Sheffield","year":"2018","journal-title":"Water Resour. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"112684","DOI":"10.1016\/j.rse.2021.112684","article-title":"Explaining discrepancies between spectral and in-situ plant diversity in multispectral satellite earth observation","volume":"265","author":"Hauser","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112349","DOI":"10.1016\/j.rse.2021.112349","article-title":"NASA\u2019s surface biology and geology designated observable: A perspective on surface imaging algorithms","volume":"257","author":"Townsend","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107610","DOI":"10.1016\/j.agwat.2022.107610","article-title":"Regional water-saving potential calculation method for paddy rice based on remote sensing","volume":"267","author":"Wei","year":"2022","journal-title":"Agric. Water Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1109\/TGRS.2003.812907","article-title":"Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality","volume":"41","author":"Brando","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1029\/JB079i011p01615","article-title":"Spectral reflectance systematics for mixtures of powdered hypersthene, labradorite, and ilmenite","volume":"79","author":"Nash","year":"1974","journal-title":"J. Geophys. Res."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"10513","DOI":"10.1029\/JB091iB10p10513","article-title":"Spectral mixture modeling: A new analysis of rock and soil types at the Viking Lander 1 site","volume":"91","author":"Adams","year":"1986","journal-title":"J. Geophys. Res."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0034-4257(94)90107-4","article-title":"Nonlinear spectral mixing models for vegetative and soil surfaces","volume":"47","author":"Borel","year":"1994","journal-title":"Remote Sens. Environ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0034-4257(91)90002-N","article-title":"A comparison of spectral reflectance properties at the needle, branch, and canopy level for selected conifer species","volume":"35","author":"Williams","year":"1991","journal-title":"Remote Sens. Environ."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","unstructured":"Halimi, A., Altmann, Y., Dobigeon, N., and Tourneret, J.-Y. (2011, January 24\u201329). Unmixing hyperspectral images using the generalized bilinear model. Proceedings of the 2011 IEEE International Geoscience and Remote Sensing Symposium, Vancouver, BC, Canada.","DOI":"10.1109\/IGARSS.2011.6049492"},{"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","unstructured":"Heylen, R., and Scheunders, P. (2015, January 2\u20135). Nonlinear Unmixing with a Multilinear Mixing Model. Proceedings of the 2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Tokyo, Japan.","DOI":"10.1109\/WHISPERS.2015.8075425"},{"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":"74770I","DOI":"10.1117\/12.830492","article-title":"Nonlinear mixture model for hyperspectral unmixing","volume":"7477","author":"Nascimento","year":"2009","journal-title":"Image Signal Process. Remote Sens. XV"},{"key":"ref_28","unstructured":"Babaie-zadeh, M., Jutten, C., and Nayebi, K. (2001, January 9\u201313). Blind separating convolutive post non-linear mixtures. Proceedings of the 3rd Workshop on Independent Component Analysis and Signal Separation (ICA2001), San Diego, CA, USA."},{"key":"ref_29","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_30","doi-asserted-by":"crossref","unstructured":"Altmann, Y., Halimi, A., Dobigeon, N., and Tourneret, J. (2011, January 24\u201329). A post nonlinear mixing model for hyperspectral images unmixing. Proceedings of the 2011 IEEE International Geoscience and Remote Sensing Symposium, Vancouver, BC, Canada.","DOI":"10.1109\/IGARSS.2011.6049491"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hapke, B. (1993). Topics in Remote Sensing\u2014Theory of Reflectance and Emittance Spectroscopy, First Paper, Cambridge University Press.","DOI":"10.1017\/CBO9780511524998"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"E617","DOI":"10.1029\/JB092iB04p0E617","article-title":"Quantitative abundance estimates from bidirectional reflectance measurements","volume":"92","author":"Mustard","year":"1987","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"13619","DOI":"10.1029\/JB094iB10p13619","article-title":"Photometric phase functions of common geologic minerals and applications to quantitative analysis of mineral mixture reflectance spectra","volume":"94","author":"Mustard","year":"1989","journal-title":"J. Geophys. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"E12001","DOI":"10.1029\/2005JE002534","article-title":"Quantifying absolute water content of minerals using near-infrared reflectance spectroscopy","volume":"110","author":"Milliken","year":"2005","journal-title":"J. Geophys. Res. E Planets"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1186\/s13065-018-0460-z","article-title":"Hapke-based computational method to enable unmixing of hyperspectral data of common salts","volume":"12","author":"Howari","year":"2018","journal-title":"Chem. Cent. J."},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"3055","DOI":"10.1029\/JB086iB04p03055","article-title":"Bidirectional reflectance spectroscopy: 2. Experiments and observations","volume":"86","author":"Hapke","year":"1981","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_38","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_39","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_40","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/36.655326","article-title":"On the errors of two estimators of sub-pixel fractional cover when mixing is linear","volume":"36","author":"Settle","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6596","DOI":"10.1364\/AO.43.006596","article-title":"Stochastic spectral unmixing with enhanced endmember class separation","volume":"43","author":"Eismann","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3725","DOI":"10.1109\/TGRS.2006.881123","article-title":"Iterative spectral unmixing for optimizing per-pixel endmember sets","volume":"44","author":"Rogge","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4112","DOI":"10.1109\/TGRS.2011.2155070","article-title":"Fully constrained least squares spectral unmixing by simplex projection","volume":"49","author":"Heylen","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5067","DOI":"10.1109\/TGRS.2015.2417162","article-title":"Minimum volume simplex analysis: A fast algorithm for linear hyperspectral unmixing","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Sahoo, M.M., Arun, P.V., and Porwal, A. (2021, January 24\u201326). Support vector machines for unmixing geological mixtures. Proceedings of the 2021 11th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing (WHISPERS), Amsterdam, The Netherlands.","DOI":"10.1109\/WHISPERS52202.2021.9484054"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3968","DOI":"10.1109\/TGRS.2012.2227757","article-title":"Spectral unmixing in multiple-kernel Hilbert space for hyperspectral imagery","volume":"51","author":"Gu","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"4568","DOI":"10.1109\/TIP.2020.2974062","article-title":"Spectral variability aware blind hyperspectral image unmixing based on convex geometry","volume":"29","author":"Drumetz","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1109\/TGRS.2011.2170999","article-title":"Geometric unmixing of large hyperspectral images: A barycentric coordinate approach","volume":"50","author":"Honeine","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0034-4257(95)00177-8","article-title":"A method for manual endmember selection and spectral unmixing","volume":"55","author":"Bateson","year":"1996","journal-title":"Remote Sens. Environ."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5412","DOI":"10.1109\/TIP.2014.2363423","article-title":"Spectral unmixing via data-guided sparsity","volume":"23","author":"Zhu","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4248","DOI":"10.1109\/TGRS.2011.2169680","article-title":"Spatially adaptive hyperspectral unmixing","volume":"49","author":"Canham","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_52","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_53","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/JSTARS.2020.2976602","article-title":"Multiple-priors ensemble constrained nonnegative matrix factorization for spectral unmixing","volume":"13","author":"Qu","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/JSTARS.2020.2977399","article-title":"Improved collaborative non-negative matrix factorization and total variation for hyperspectral unmixing","volume":"13","author":"Yuan","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.isprsjprs.2016.02.006","article-title":"Area-to-point regression kriging for pan-sharpening","volume":"114","author":"Wang","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.rse.2015.06.003","article-title":"Downscaling MODIS images with area-to-point regression kriging","volume":"166","author":"Wang","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2014.02.012","article-title":"Sub-pixel mapping of remote sensing images based on radial basis function interpolation","volume":"92","author":"Wang","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"111817","DOI":"10.1016\/j.rse.2020.111817","article-title":"Sub-pixel mapping with point constraints","volume":"244","author":"Wang","year":"2020","journal-title":"Remote Sens. Environ."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1109\/JSTARS.2013.2280063","article-title":"Non-local sparse unmixing for hyperspectral remote sensing imagery","volume":"7","author":"Zhong","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_60","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":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"8766","DOI":"10.1109\/TGRS.2020.2990476","article-title":"Spectral\u2013spatial-weighted multiview collaborative sparse unmixing for hyperspectral images","volume":"58","author":"Qi","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"114843","DOI":"10.1016\/j.cam.2022.114843","article-title":"Reweighted sparse unmixing for hyperspectral images with noise level estimation","volume":"421","author":"Wang","year":"2023","journal-title":"J. Comput. Appl. Math."},{"key":"ref_63","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_64","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_65","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":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_66","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_67","doi-asserted-by":"crossref","first-page":"2991","DOI":"10.1109\/TIP.2019.2893068","article-title":"Nonconvex-sparsity and nonlocal-smoothness-based blind hyperspectral unmixing","volume":"28","author":"Yao","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1109\/LGRS.2012.2215835","article-title":"A sparse NMF-SU for seismic random noise attenuation","volume":"10","author":"Tian","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_69","first-page":"50","article-title":"Blind spectral unmixing by local maximization of non-Gaussianity","volume":"88","author":"Caiafa","year":"2008","journal-title":"Signal"},{"key":"ref_70","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."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"4915","DOI":"10.1109\/TGRS.2020.2968541","article-title":"Matrix cofactorization for joint spatial\u2013spectral unmixing of hyperspectral images","volume":"58","author":"Lagrange","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF01032888","article-title":"Fuzzy Qmodel-A new approach for linear unmixing","volume":"14","author":"Full","year":"1982","journal-title":"Math. Geol."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Arun, P.V., Buddhiraju, K.M., and Porwal, A. (2016, January 21\u201324). Integration of contextual knowledge in unsupervised sub-pixel classification. Proceedings of the 2016 8th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Los Angeles, CA, USA.","DOI":"10.1109\/WHISPERS.2016.8071663"},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Arun, P.V., and Buddhiraju, K.M. (2016, January 10\u201315). Classification and clustering perspective towards spectral unmxing. Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China.","DOI":"10.1109\/IGARSS.2016.7730605"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.rse.2017.10.020","article-title":"Regional clustering-based spatial preprocessing for hyperspectral unmixing","volume":"204","author":"Xu","year":"2018","journal-title":"Remote Sens. Environ."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"3629","DOI":"10.1080\/014311697216847","article-title":"Comparison of fuzzy c-means classification, linear mixture modelling and MLC probabilities as tools for unmixing coarse pixels","volume":"18","author":"Bastin","year":"1997","journal-title":"Int. J. Remote Sens."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1109\/JSTARS.2011.2181340","article-title":"Automated extraction of image-based endmember bundles for improved spectral unmixing","volume":"5","author":"Somers","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"4844","DOI":"10.1109\/TGRS.2019.2893489","article-title":"Nonlinear hyperspectral unmixing with graphical models","volume":"57","author":"Heylen","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1109\/LGRS.2016.2560222","article-title":"Hopfield neural network approach for supervised nonlinear spectral unmixing","volume":"13","author":"Li","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"2812","DOI":"10.1109\/TGRS.2015.2506168","article-title":"A novel spectral unmixing method incorporating spectral variability within endmember classes","volume":"54","author":"Uezato","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1080\/014311697218845","article-title":"Non-linear mixture modelling without end-members using an artificial neural network","volume":"18","author":"Foody","year":"1997","journal-title":"Int. J. Remote Sens."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1109\/36.921417","article-title":"Comparison of the multilayer perceptron with neuro-fuzzy techniques in the estimation of cover class mixture in remotely sensed data","volume":"39","author":"Baraldi","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Plaza, J., Plaza, A., P\u00e9rez, R., and Mart\u00ednez, P. (2007, January 23\u201328). Joint linear\/nonlinear spectral unmixing of hyperspectral image data. Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS), Barcelona, Spain.","DOI":"10.1109\/IGARSS.2007.4423735"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1109\/36.957296","article-title":"A quantitative and comparative analysis of linear and nonlinear spectral mixture models using radial basis function neural networks","volume":"39","author":"Guilfoyle","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_85","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_86","doi-asserted-by":"crossref","unstructured":"Licciardi, G.A., Ceamanos, X., Dout\u00e9, S., and Chanussot, J. (2012, January 22\u201327). Unsupervised nonlinear spectral unmixing by means of NLPCA applied to hyperspectral imagery. Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium, Munich, Germany.","DOI":"10.1109\/IGARSS.2012.6351281"},{"key":"ref_87","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_88","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1109\/TGRS.2018.2868690","article-title":"uDAS: An untied denoising autoencoder with sparsity for spectral unmixing","volume":"57","author":"Qu","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"5527214","DOI":"10.1109\/TGRS.2022.3168712","article-title":"Deep generative model for spatial\u2013spectral unmixing with multiple endmember priors","volume":"60","author":"Shi","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_90","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_91","doi-asserted-by":"crossref","first-page":"6518","DOI":"10.1109\/TNNLS.2021.3082289","article-title":"Endmember-guided unmixing network (EGU-Net)- A general deep learning framework for self-supervised hyperspectral unmixing","volume":"33","author":"Hong","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"7418","DOI":"10.1109\/TGRS.2020.2982490","article-title":"Spectral mixture model inspired network architectures for hyperspectral unmixing","volume":"58","author":"Qian","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_93","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_94","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1109\/TGRS.2020.2992743","article-title":"Convolutional autoencoder for spectral-spatial hyperspectral unmixing","volume":"59","author":"Palsson","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"25646","DOI":"10.1109\/ACCESS.2018.2818280","article-title":"Hyperspectral unmixing using a neural network autoencoder","volume":"6","author":"Palsson","year":"2018","journal-title":"IEEE Access"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.neucom.2018.05.051","article-title":"CNN based sub-pixel mapping for hyperspectral images","volume":"311","author":"Arun","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_97","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":"Pattathal","year":"2022","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"1996","DOI":"10.1109\/LGRS.2020.3011941","article-title":"Deep half-siamese networks for hyperspectral unmixing","volume":"18","author":"Han","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1109\/LGRS.2018.2857804","article-title":"Hyperspectral unmixing via deep convolutional neural networks","volume":"15","author":"Zhang","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/S0034-4257(96)00122-8","article-title":"Optimization of endmembers for spectral mixture analysis","volume":"59","author":"Tompkins","year":"1997","journal-title":"Remote Sens. Environ."},{"key":"ref_101","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_102","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1109\/JSTARS.2012.2189556","article-title":"Spectral unmixing cluster validity index for multiple sets of endmembers","volume":"5","author":"Anderson","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_103","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_104","unstructured":"Boardman, J.W., Kruse, F.A., and Green, R.O. (1995, January 23\u201326). Mapping target signatures via partial unmixing of AVIRIS data. Proceedings of the Fifth JPL Airborne Geoscience Workshop, Pasadena, CA, USA. Available online: http:\/\/hdl.handle.net\/2014\/33635."},{"key":"ref_105","unstructured":"Singer, R.B., and McCord, T.B. (1979, January 19\u201323). Mars: Large scale mixing of bright and dark surface materials and implications for analysis of spectral reflectance. Proceedings of the 10th Lunar and Planetary Science Conference, Houston, TX, USA."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Altmann, Y., Halimi, A., Dobigeon, N., and Tourneret, J.-Y. (2011, January 22\u201327). Supervised nonlinear spectral unmixing using a polynomial post nonlinear model for hyperspectral imagery. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5946577"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/S0304-3800(99)00100-3","article-title":"Support vector machines for optimal classification and spectral unmixing","volume":"120","author":"Brown","year":"1999","journal-title":"Ecol. Model."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/LGRS.2013.2262371","article-title":"Spectral unmixing model based on least squares support vector machine with unmixing residue constraints","volume":"10","author":"Wang","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2113\/gselements.9.2.99","article-title":"Serpentinite: What, why, where?","volume":"9","author":"Evans","year":"2013","journal-title":"Elements"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.2113\/gsecongeo.74.7.1613","article-title":"Spectra of altered rocks in the visible and near infrared","volume":"74","author":"Hunt","year":"1979","journal-title":"Econ. Geol."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0034-4257(93)90023-Q","article-title":"Relationships of soil, grass, and bedrock over the kaweah serpentinite melange through spectral mixture analysis of AVIRIS data","volume":"44","author":"Mustard","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"13997","DOI":"10.1029\/JB094iB10p13997","article-title":"Spectral characteristics of chlorites and Mg-serpentines using high- resolution reflectance spectroscopy","volume":"94","author":"King","year":"1989","journal-title":"J. Geophys. Res."},{"key":"ref_113","first-page":"23","article-title":"Visible and near infrared spectra of minerals and rocks: II. Carbonates","volume":"2","author":"Hunt","year":"1971","journal-title":"Modern Geol."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0371-1951(58)80094-6","article-title":"High-resolution, temperature-dependent spectra of calcite","volume":"10","author":"Hexter","year":"1958","journal-title":"Spectrochim. Acta"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1190\/1.1440721","article-title":"Spectral signatures of particulate minerals in the visible and near infrared","volume":"42","author":"Hunt","year":"1977","journal-title":"Geophysics"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.geoderma.2006.07.004","article-title":"Determining the composition of mineral-organic mixes using UV-vis-NIR diffuse reflectance spectroscopy","volume":"137","author":"Rossel","year":"2006","journal-title":"Geoderma"},{"key":"ref_117","doi-asserted-by":"crossref","unstructured":"Haldar, S.K. (2020). Introduction to Mineralogy and Petrology, Elsevier.","DOI":"10.1016\/B978-0-12-820585-3.00004-1"},{"key":"ref_118","unstructured":"Adams, J.B., and Goullaud, L.H. (1978, January 13\u201317). Plagioclase feldspars: Visible and near infrared diffuse reflectance spectra as applied to remote sensing. Proceedings of the Lunar and Planetary Science Conference Proceedings, Houston, TX, USA."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"5120","DOI":"10.1029\/2003JE002127","article-title":"Visible\/near-infrared spectra of experimentally shocked plagioclase feldspars","volume":"108","author":"Johnson","year":"2003","journal-title":"J. Geophys. Res. Planets"},{"key":"ref_120","unstructured":"Karr, C. (1975). Proceedings of the Infrared and Raman Spectroscopy of Lunar and Terrestrial Minerals, Academic Press, Inc."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3300\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:02:09Z","timestamp":1760126529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,27]]},"references-count":120,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["rs15133300"],"URL":"https:\/\/doi.org\/10.3390\/rs15133300","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,27]]}}}