A Sturdy Nonlinear Hyperspectral Unmixing

References

• K. E. Themelis, F. Schmidt, O. Sykioti, A. A. Rontogiannis, K. D. Koutroumbas, and I. A. Daglis, “On the unmixing of MEx/OMEGA hyperspectral data,” Planet. Space Sci., Vol. 68, no. 1, pp. 34–41, 2012.
   Web of Science ®Google Scholar
• A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging: An emerging process analytical tool for food quality and safety control,” Trends in Food Sci. & Techn, Vol. 18, no. 12, pp. 590–598, 2007.
   Web of Science ®Google Scholar
• G. P. Asner, and K. B. Heidebrecht, “Spectral unmixing of vegetation, soil and dry carbon cover in arid regions: Comparing multispectral and hyperspectral observations,” I. J. Remote Sens, Vol. 23, no. 19, pp. 3939–3958, 2002.
   Web of Science ®Google Scholar
• N. Dobigeon, and N. Brun, “Spectral mixture analysis of EELS spectrum images,” Ultramicroscopy, Vol. 120, pp. 25–34, 2012.
   PubMed Web of Science ®Google Scholar
• N. Keshava, and J. F. Mustard, “Spectral unmixing,” IEEE Signal Proces. Magaz, Vol. 19, no. 1, pp. 44–57, 2002.
   Web of Science ®Google Scholar
• J. M. Bioucas-Dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 5, no. 2, pp. 354–379, s2012.
   Web of Science ®Google Scholar
• R. Heylen, M. Parente, and P. Gader, “A review of nonlinear hyperspectral unmixing methods,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 7, no. 6, pp. 1844–1868, s2014.
   Web of Science ®Google Scholar
• N. Dobigeon, J.-Y. Tourneret, C. Richard, J. C. M. Bermudez, S. McLaughlin, and A. O. Hero, “Nonlinear unmixing of hyperspectral images: Models and algorithms,” IEEE Signal Proces. Magaz, Vol. 31, no. 1, pp. 82–94, 2014.
   Web of Science ®Google Scholar
• A. Halimi, Y. Altmann, N. Dobigeon, and J.-Y. Tourneret, “Nonlinear unmixing of hyperspectral images using a generalized bilinear model,” IEEE Trans. Geosci. Remote Sens, Vol. 49, no. 11, pp. 4153–4162, 2011.
   Web of Science ®Google Scholar
• A. Halimi, Y. Altmann, N. Dobigeon, and J.-Y. Tourneret, “Unmixing hyperspectral images using the generalized bilinear model,” Proc. of IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), pp. 1886–1889, 2011.
   Google Scholar
• J. M. P. Nascimento, and J. M. Bioucas-Dias, “Nonlinear mixture model for hyperspectral unmixing,” Proc. of SPIE, Vol. 7477, pp. 74770I, Sep. 2009.
   Google Scholar
• W. Fan, B. Hu, J. Miller, and M. Li, “Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated-forest hyperspectral data,” Int. J. Remote Sens., Vol. 30, no. 11, pp. 2951–2962, 2009.
   Web of Science ®Google Scholar
• I. Meganem, P. Deliot, X. Briottet, Y. Deville, and S. Hosseini, “Linear-quadratic mixing model for reflecta-nces in urban environments,” IEEE Trans. Geosci. Remote Sens, Vol. 52, no. 1, pp. 544–558, Jan. 2014.
   Web of Science ®Google Scholar
• Y. Altmann, A. Halimi, N. Dobigeon, and J.-Y. Tourneret, “Supervised nonlinear spectral unmixing using a post nonlinear mixing model for hyperspectral imagery,” IEEE Trans. Image Process, Vol. 21, no. 6, pp. 3017–3025, 2012.
   PubMed Web of Science ®Google Scholar
• B. Somers, K. Cools, S. Delalieux, J. Stuckens, D. V. der Zande, W. W. Verstraeten, and P. Coppin, “Nonlinear hyperspectral mixture analysis for tree cover estimates in orchards,” Remote Sens. Environ., Vol. 113, pp. 1183–1193, 2009.
   Web of Science ®Google Scholar
• B. Somers, L. Tits, and P. Coppin, “Quantifying nonlinear spectral mixing in vegetated areas: Computer simulation model validation and first results,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 7, no. 6, pp. 1956–1965, 2014.
   Web of Science ®Google Scholar
• Y. Altmann, N. Dobigeon, and J.-Y. Tourneret. “Bilinear models for nonlinear unmixing of hyperspectral images,” Proc. of IEEE GRSS Workshop Hyperspectral Image Signal Process.: Evolution in Remote Sens. (WHISPERS), Lisbon, Portugal, pp. 1–4, 2011.
   Google Scholar
• Y. Altmann, A. Halimi, N. Dobigeon, and J.-Y. Tourneret, “Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery,” IEEE Trans. Image Process, Vol. 21, no. 6, pp. 3017–3025, 2012.
   PubMed Web of Science ®Google Scholar
• N. Dobigeon, L. Tits, B. Somers, Y. Altmann, and P. Coppin, “A comparison of nonlinear mixing models for vegetated areas using simulated and real hyperspectral data,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 7, no. 6, pp. 1869–1878, 2014.
   Web of Science ®Google Scholar
• N. Dobigeon, J.-Y. Tourneret, C. Richard, J. C. M. Bermudez, S. McLaughlin, and A. O. Hero, “Nonlinear unmixing of hyperspectral images: Models and algorithms,” IEEE Signal Proces. Magaz, Vol. 31, no. 1, pp. 89–94, 2014.
   Web of Science ®Google Scholar
• R. Heylen, M. Parente, and P. Gader, “A review of nonlinear hyperspectral unmixing methods,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 7, no. 6, pp. 1844–1868, 2014.
   Web of Science ®Google Scholar
• B. Somers, G. P. Asner, L. Tits, and P. Coppin, “Endmember variability in spectral mixture analysis: A review,” Remote Sensing Environment, Vol. 115, no. 7, pp. 1603–1616, 2011.
   Web of Science ®Google Scholar
• A. Zare, and K. Ho, “Endmember variability in hyperspectral analysis: Addressing spectral variability during spectral unmixing,” IEEE Signal Process Mag., Vol. 31, no. 1, pp. 95–104, 2014.
   Web of Science ®Google Scholar
• A. Halimi, N. Dobigeon, and J.-Y. Tourneret, “Unsupervised unmixing of hyperspectral images accounting for endmember variability,” IEEE Trans. Image Process, Vol. 24, no. 12, pp. 4904–4917, 2015.
   PubMed Web of Science ®Google Scholar
• D. A. Roberts, M. Gardner, R. Church, S. Ustin, G. Scheer, and R. O. Green, “Mapping chaparral in the Santa Monica Mountains using multiple endmember spectral mixture models,” Remote Sens. Environ, Vol. 65, no. 3, pp. 267–279, 1998.
   Web of Science ®Google Scholar
• C. A. Bateson, G. P. Asner, and C. A. Wessman, “Endmember bundles: A new approach to incorporating endmember variability into spectral mixture analysis,” IEEE Trans. Geosci. Remote Sens, Vol. 38, no. 2, pp. 1083–1094, 2000.
   Web of Science ®Google Scholar
• M. Goenaga, M. Torres-Madronero, M. Velez-Reyes, S. J. Van Bloem, and J. D. Chinea, “Unmixing analysis of a time series of hyperion images over the Guánica dry forest in Puerto Rico,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 6, no. 2, pp. 329–338, 2013.
   Web of Science ®Google Scholar
• B. Somers, M. Zortea, A. Plaza, and G. Asner, “Automated extraction of image-based endmember bundles for improved spectral unmixing,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 5, no. 2, pp. 396–408, 2012.
   Web of Science ®Google Scholar
• J. M. P. Nascimento, and J. M. Bioucas Dias, “Does independent component analysis play a role in unmixing hyperspectral data,” IEEE Trans. Geosci. Remote Sens, Vol. 43, no. 1, pp. 175–187, Jan. 2005.
   Web of Science ®Google Scholar
• M. A. Veganzones, et al. “A new extended linear mixing model to address spectral variability,” Proceedings of IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, Lausanne, Switzerland, pp. 1–4, 2014.
   Google Scholar
• G. A. Shaw, and H.-H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Lab. J, Vol. 14, no. 1, pp. 3–28, 2003.
   Google Scholar
• O. Eches, N. Dobigeon, C. Mailhes, and J.-Y. Tourneret, “Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery,” IEEE Trans. Imag. Proc., Vol. 19, no. 6, pp. 1403–1413, 2010.
   PubMed Web of Science ®Google Scholar
• A. Zare, P. Gader, and G. Casella, “Sampling piecewise convex unmixing and endmember extraction,” IEEE Trans. Geosci. Remote Sens, Vol. 51, no. 3, pp. 1655–1665, 2013.
   Web of Science ®Google Scholar
• D. Stein. “Application of the normal compositional model to the analysis of hyperspectral imagery,” Proc. of IEEE Workshop Adv. Techn. Anal. Remotely Sensed Data, 2003, pp. 44–51.
   Google Scholar
• X. Du, A. Zare, P. Gader, and D. Dranishnikov, “Spatial and spectral unmixing using the beta compositional model,” IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens, Vol. 7, no. 6, pp. 1994–2003, Jun. 2014.
   Web of Science ®Google Scholar
• J. M. P. Nascimento, and J. M. Bioucas-Dias, “Vertex component analysis: A fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens, Vol. 43, no. 4, pp. 898–910, 2005.
   Web of Science ®Google Scholar
• M. Winter. “Fast autonomous spectral end-member determination in hyperspectral data,” Proc. of 13th Int. Conf. Appl. Geologic Remote Sens., vol. 2. Vancouver, BC, Canada, Apr. 1999, pp. 337–344.
   Google Scholar
• D. C. Heinz, and C.-I. Chang, “Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens, Vol. 29, no. 3, pp. 529–545, 2001.
   Google Scholar
• J. Bioucas-Dias, and M. A. T. Figueiredo. “Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing,” Proc. of 2nd Workshop Hyperspectral Image Signal Process., Evol. Remote Sens. (WHISPERS), 2010, pp. 1–4.
   Google Scholar
• Y. Altmann, M. Pereyra, and S. McLaughlin, “Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis,” IEEE Trans. Image Process, Vol. 1, no. 3, pp. 174–185, 2015.
   Google Scholar
• J. Chen, C. Richard, and P. Honeine, “Nonlinear unmixing of hyperspectral data based on a linear-mixture/nonlinear-fluctuation model,” IEEE Trans. Signal Process, Vol. 61, no. 2, pp. 480–492, 2013.
   Web of Science ®Google Scholar
• Y. Altmann, S. McLaughlin, and A. Hero, “Robust linear spectral unmixing using anomaly detection,” IEEE Trans. Comput. Imag, Vol. 1, no. 2, pp. 74–85, 2015.
   Web of Science ®Google Scholar
• R. Close, P. Gader, J. Wilson, and A. Zare. “Using physics-based macroscopic and microscopic mixture models for hyperspectral pixel unmixing,” Proc. of SPIE Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVIII, S. S. Shen and P. E. Lewis, Eds., vol. 8390. Baltimore, Maryland, USA: SPIE, 2012.
   Google Scholar
• A. A. Kalaitzis, and N. D. Lawrence. “Residual component analysis,” Proc. of ICML, 2012, pp. 1–3.
   Google Scholar
• J. Sigurdsson, M. O. Ulfarsson, and J. R. Sveinsson, “Hyperspectral unmixing with lq-regularization,” IEEE Trans. Geosci. Remote Sens, Vol. 52, no. 11, pp. 6793–6806, 2014.
   Web of Science ®Google Scholar
• A. Halimi, C. Mailhes, J.-Y. Tourneret, and H. Snoussi, “Bayesian estimation of smooth altimetric parameters: Application to conventional and delay/Doppler altimetry,” IEEE Trans. Geosci. Remote Sens, Vol. 54, no. 4, pp. 2207–2219, 2016.
   Web of Science ®Google Scholar
• A. Halimi, and P. Honeine, “Hyperspectral unmixing in presence of endmember variability, nonlinearity and mismodelling effects,” IEEE Trans. Imag. Proc., Vol. 25, no. 10, pp. 4565–4579, 2016.
   PubMed Web of Science ®Google Scholar
• M. V. Sireesha, P. V. Naganjaneyulu, and K. Babulu, “A sturdy nonlinear hyperspectral unmixing algorithm using iterative block coordinate descent algorithm,” I. J. Intel. Eng. Syst, Vol. 12, no. 3, pp. 166–177, 2019.
   Google Scholar
• P.-A. Thouvenin, N. Dobigeon, and J.-Y. Tourneret, “Hyperspectral unmixing with spectral variability using a perturbed linear mixing model,” IEEE Trans. Signal Process, Vol. 64, no. 2, pp. 525–538, 2016.
   Web of Science ®Google Scholar
• P. Sprechmann, A. Bronstein, and G. Sapiro. “Real-time online singing voice separation from monaural recordings using robust low-rank modelling,” Proc. of Int. Soc. Music Information Retrieval Conf. (ISMIR), Porto, Portugal, 2012.
   Google Scholar
• L. Zhang, Z. Chen, M. Zheng, and X. He, “Robust nonnegative matrix factorization,” Front. Electr. Electron. Eng. China, Vol. 6, no. 2, pp. 192–200, 2011.
   Google Scholar
• B. Shen, L. Si, R. Ji, and B. Liu, “Robust nonnegative matrix factorization via L1 norm regularization,” ArXiv preprint (2012).
   Google Scholar
• D. Kong, C. Ding, and H. Huang. “Robust nonnegative matrix factorization using L2,1-norm,” Proc. of 20th ACM Int. Conf. Information and Knowledge Management, New York, USA, 2011, pp. 673–682.
   Google Scholar
• A. Ben Hamza, and D. J. Brady, “Reconstruction of reflectance spectra using robust nonnegative matrix factorizations,” IEEE Trans. Signal Process, Vol. 54, pp. 3637–3642, 2006.
   Web of Science ®Google Scholar
• S. Ghosh, and K. N. Chaudhury, “Fast separable nonlocal means,” J. Electron. Imag, Vol. 25, no. 2, pp. 023026, 2016.
   Web of Science ®Google Scholar
• S. Ghosh, and K. N. Chaudhury, “Artifact reduction for separable nonlocal means,” J. Electron. Imag, Vol. 26, no. 6, pp. 063012, 2017.
   Web of Science ®Google Scholar
• Y. S. Kim, H. Lim, O. Choi, K. Lee, J. D. K. Kim, and C. Kim. “Separable bilateral non-local means,” Proc. of IEEE I. Conf. Imag. Proc., Brussels, Belgium, pp. 1513–1516, 2011.
   Google Scholar
• C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Statist, Vol. 9, pp. 1135–1151, 1981.
   Web of Science ®Google Scholar
• T. Blu, and F. Luisier, “The SURE-LET approach to image denoising,” IEEE Trans. Imag. Proc., Vol. 16, no. 11, pp. 2778–2786, 2007.
   PubMed Web of Science ®Google Scholar
• R. Deriche. “Recursively implementing the Gaussian and its derivatives,” Proc. of IEEE I. Conf. Imag. Proc., pp. 263–26, 1992.
   Google Scholar
• ENVI User’s Guide Version 4.0. Boulder, CO, USA, RSI Research Systems Inc., Sep. 2003.
   Google Scholar
• Jet Propulsion Lab. (JPL). “AVIRIS free data,” California Inst. Technol., Pasadena, CA, 2006. [Online]. Available: http://aviris.jpl.nasa.gov/html/ aviris.freedata.html.
   Google Scholar
• H. K. Aggarwal, and A. Majumdar, “Hyperspectral unmixing in the presence of mixed noise using joint sparsity and total variation,” IEEE J. Selec. Topics Appl. Earth Observat. Remote Sens, Vol. 9, no. 9, pp. 4257–4266, 2016.
   Web of Science ®Google Scholar