Gillis, Nicolas ; Université de Mons > Faculté Polytechnique > Service de Mathématique et Recherche opérationnelle
Dobigeon, Nicolas
Language :
English
Title :
Provably robust blind source separation of linear-quadratic near-separable mixtures
Publication date :
10 September 2021
Journal title :
SIAM Journal on Imaging Sciences
Publisher :
Society for Industrial and Applied Mathematics, Philadelphia, Panama
Volume :
14
Issue :
4
Pages :
1848-1889
Peer reviewed :
Peer reviewed
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R450 - Institut NUMEDIART pour les Technologies des Arts Numériques
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H. Akbari, K. Uto, Y. Kosugi, K. Kojima, and N. Tanaka, Cancer detection using infrared hyper-spectral imaging, Cancer Sci., 102 (2011), pp. 852–857.
Y. Altmann, A. Halimi, N. Dobigeon, and J.-Y. Tourneret, Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery, IEEE Trans. Image Process., 21 (2012), pp. 3017–3025.
U. Araújo, B. Saldanha, R. Galvão, T. Yoneyama, H. Chame, and V. Visani, The successive projections algorithm for variable selection in spectroscopic multicomponent analysis, Chemom. Intell. Lab. Syst., 57 (2001), pp. 65–73.
S. Arora, R. Ge, R. Kannan, and A. Moitra, Computing a nonnegative matrix factorization – provably, in Proceedings of the 44th Annual Symposium on Theory of Computing (STOC ’12), 2012, pp. 145–162.
S. Arora, R. Ge, R. Kannan, and A. Moitra, Computing a nonnegative matrix factorization— provably, SIAM J. Comput., 45 (2016), pp. 1582–1611, https://doi.org/10.1137/130913869.
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. Top. Appl. Earth Obs. Remote Sens., 5 (2012), pp. 354–379.
J. Bobin, J. Rapin, A. Larue, and J.-L. Starck, Sparsity and adaptivity for the blind separation of partially correlated sources., IEEE Trans. Signal Process., 63 (2015), pp. 1199–1213.
P. Comon and C. Jutten, Handbook of Blind Source Separation: Independent Component Analysis and Applications, Academic Press, San Diego, CA, 2010.
Y. Deville, From separability/identifiability properties of bilinear and linear-quadratic mixture matrix factorization to factorization algorithms, Digit. Signal Process., 87 (2019), pp. 21–33.
Y. Deville and L. T. Duarte, An overview of blind source separation methods for linear-quadratic and post-nonlinear mixtures, in International Conference on Latent Variable Analysis and Signal Separation, Springer, Cham, 2015, pp. 155–167.
N. Dobigeon, Y. Altmann, N. Brun, and S. Moussaoui, Linear and nonlinear unmixing in hyper-spectral imaging, in Data Handling in Science and Technology, Vol. 30, Elsevier, Amsterdam, 2016, pp. 185–224.
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. Top. Appl. Earth Obs. Remote Sens., 7 (2014), pp. 1869–1878.
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 Process.
E. Esser, M. Moller, S. Osher, G. Sapiro, and J. Xin, A convex model for nonnegative matrix factorization and dimensionality reduction on physical space, IEEE Trans. Image Process., 21 (2012), pp. 3239–3252.
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., 30 (2009), pp. 2951–2962.
X. Fu, K. Huang, N. D. Sidiropoulos, and W.-K. Ma, Nonnegative matrix factorization for signal and data analytics: Identifiability, algorithms, and applications, IEEE Signal Process. Mag., 36 (2019), pp. 59–80.
N. Gillis, Sparse and unique nonnegative matrix factorization through data preprocessing, J. Mach. Learn. Res., 13 (2012), pp. 3349–3386.
N. Gillis, Successive nonnegative projection algorithm for robust nonnegative blind source separation, SIAM J. Imaging Sci., 7 (2014), pp. 1420–1450, https://doi.org/10.1137/130946782.
N. Gillis, Successive projection algorithm robust to outliers, in 8th International IEEE Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2019, pp. 331–335.
N. Gillis, Nonnegative Matrix Factorization, SIAM, Philadelphia, 2020, https://doi.org/10.1137/1. 9781611976410.
N. Gillis and R. Luce, Robust near-separable nonnegative matrix factorization using linear optimization, J. Mach. Learn. Res., 15 (2014), pp. 1249–1280.
N. Gillis and S. A. Vavasis, Fast and robust recursive algorithms for separable nonnegative matrix factorization, IEEE Trans. Pattern Anal. Mach. Intell., 36 (2013), pp. 698–714.
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., 49 (2011), pp. 4153– 4162.
R. Heylen, M. Parente, and P. Gader, A review of nonlinear hyperspectral unmixing methods, IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 7 (2014), pp. 1844–1868.
D. Hong, L. Gao, J. Yao, N. Yokoya, J. Chanussot, U. Heiden, and B. Zhang, Endmember-guided unmixing network (EGU-Net): A general deep learning framework for self-supervised hyperspectral unmixing, IEEE Trans. Neural Netw. Learn. Syst., (2021), https://doi.org/10.1109/TNNLS.2021. 3082289.
M.-D. Iordache, J. M. Bioucas-Dias, and A. Plaza, Total variation spatial regularization for sparse
hyperspectral unmixing, IEEE Trans. Geosci. Remote Sens., 50 (2012), pp. 4484–4502. [27] I. Jolliffe, Principal Component Analysis, Spring-Verlag, New York, 1986.
C. Kervazo and J. Bobin, Stacked Sparse Blind Source Separation for Non-linear Mixtures, https://hal.archives-ouvertes.fr/hal-02091102/, 2019.
C. Kervazo, J. Bobin, C. Chenot, and F. Sureau, Use of PALM for ℓ1 sparse matrix factorization: Difficulty and rationalization of an heuristic approach, Digit. Signal Process., 97 (2020), 102611, https://doi.org/10.1016/j.dsp.2019.102611.
M. Kowalski, Sparse regression using mixed norms, Appl. Comput. Harmon. Anal., 27 (2009), pp. 303– 324.
D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization, Nature, 401 (1999), pp. 788–791.
W.-K. Ma, J. M. Bioucas-Dias, T.-H. Chan, N. Gillis, P. Gader, A. J. Plaza, A. Ambikapathi, and C.-Y. Chi, A signal processing perspective on hyperspectral unmixing: Insights from remote sensing, IEEE Signal Process. Mag., 31 (2013), pp. 67–81.
I. Meganem, P. Déliot, X. Briottet, Y. Deville, and S. Hosseini, Linear–quadratic mixing model for reflectances in urban environments, IEEE Trans. Geosci. Remote Sens., 52 (2013), pp. 544–558.
I. Meganem, Y. Deville, S. Hosseini, P. Deliot, and X. Briottet, Linear-quadratic blind source separation using NMF to unmix urban hyperspectral images, IEEE Trans. Signal Process., 62 (2014), pp. 1822–1833.
J. M. Nascimento and J. M. Bioucas-Dias, Hyperspectral unmixing based on mixtures of Dirichlet components, IEEE Trans. Geosci. Remote Sens., 50 (2011), pp. 863–878.
J. M. P. Nascimento and J. M. Bioucas-Dias, Nonlinear Mixture Model for Hyperspectral Unmixing, SPIE 7477, L. Bruzzone, C. Notarnicola, and F. Posa, eds., SPIE, Bellingham, WA, 2009.
J. M. Nascimento and J. M. Dias, Vertex component analysis: A fast algorithm to unmix hyperspectral data, IEEE Trans. Geosci. Remote Sens., 43 (2005), pp. 898–910.
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Appl. Optim. 87, Springer Science & Business Media, New York, 2013.
B. Palsson, M. O. Ulfarsson, and J. R. Sveinsson, Convolutional autoencoder for spatial-spectral hy-perspectral unmixing, in International Geoscience and Remote Sensing Symposium (IGARSS), IEEE, 2019, pp. 357–360.
B. Recht, C. Re, J. Tropp, and V. Bittorf, Factoring nonnegative matrices with linear programs, in Advances in Neural Information Processing Systems, MIT Press, Cambridge, UK, 2012, pp. 1214– 1222.
O. Y. Rodionova, L. P. Houmøller, A. L. Pomerantsev, P. Geladi, J. Burger, V. L. Doro-feyev, and A. P. Arzamastsev, NIR spectrometry for counterfeit drug detection: A feasibility study, Anal. Chim. Acta, 549 (2005), pp. 151–158.
M. E. Schaepman, S. L. Ustin, A. J. Plaza, T. H. Painter, J. Verrelst, and S. Liang, Earth system science related imaging spectroscopy—an assessment, Remote Sens. Environ., 113 (2009), pp. S123–S137.
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., 113 (2009), pp. 1183–1193.
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., 68 (2012), pp. 34– 41.
S. A. Vavasis, On the complexity of nonnegative matrix factorization, SIAM J. Optim., 20 (2010), pp. 1364–1377, https://doi.org/10.1137/070709967.
M. Zibulevsky and B. A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary, Neural Comput., 13 (2001), pp. 863–882.