Abstract
This paper presents a geometric method for solving the Blind Source Separation problem. The method is based on a weak sparsity assumption: for each source, there should exist at least one pair of zones that share only this source. The process consists first in finding the pairs of zones sharing a unique source with an original geometric approach. Each pair of zones, having a mono-dimensional intersection, yields an estimate of a column of the mixing matrix up to a scale factor. All intersections are identified by Singular Value Decomposition. The intersections corresponding to the same column of the mixing matrix are then grouped by a clustering algorithm so as to derive a single estimate of each column. The sources are finally reconstructed from the observed vectors and mixing parameters with a least square algorithm. Various tests on synthetic and real hyperspectral astrophysical data illustrate the efficiency of this approach.
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Abrard, F., Deville, Y.: A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources. Sig. Process. 85(7), 1389–1403 (2005)
Benachir, D., Deville, Y., Hosseini, S.: Blind spatial unmixing of multispectral images: an approach based on two-source sparsity and geometrical properties. In: IEEE International Conference on ICASSP, pp. 3171–3175 (2014)
Berné, O., Joblin, C., Deville, Y., Smith, J.D., Rapacioli, M., Bernard, J.P., Thomas, J., Reach, W., Abergel, A.: Analysis of the emission of very small dust particles from spitzer spectro-imagery data using blind signal separation methods. Astron. Astrophys. 469, 575–586 (2007)
Bioucas-dias, J.M., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P., Chanussot, J.: Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012)
Boulais, A., Deville, Y., Berné, O.: A geometrical blind separation method for unconstrained-sum locally dominant sources. In: IEEE International Workshop ECMSM (2015)
Cichocki, A., Zdunek, R., Phan, A., Amari, S.I.: Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation. Wiley, New Year (2009)
Comon, P., Jutten, C. (eds.): Handbook of Blind Source Separation: Independent Component Analysis and Applications. Elsevier, Oxford (2010)
Deville, Y.: Chapter 6, Sparse component analysis: a general framework for linear and nonlinear blind source separation and mixture identification. In: Naik, G.R., Wang, W. (eds.) Blind Source Separation: Advances in Theory, Algorithms and Applications, pp. 151–196. Springer, Heidelberg (2014)
Deville, Y.: Blind source separation and blind mixture identification methods. In: Wiley Encyclopedia of Electrical and Electronics Engineering. Wiley, New York (2016).
Golub, G.H., Van Loan, C.H.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltmore (1996)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing, Chapter 10: Image Segmentation. Prentice-Hall Inc., New Jersey (2006)
Gribonval, R., Lesage, S.: A survey of sparse component analysis for blind source separation: principles, perspectives, and new challenges. In: ESANN 2006 Proceedings, pp. 323–330 (2006)
He, Z., Cichocki, A., Li, Y., Xie, S., Sanei, S.: K-hyperline clustering learning for sparse component analysis. Sig. Process. 89, 1011–1022 (2009)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley-Interscience, New Jersey (2001)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Meganem, I., Deville, Y., Puigt, M.: Blind separation methods based on correlation for sparse possibly-correlated images. In: IEEE International Conference on ICASSP, pp. 1334–1337 (2010)
Naeini, F., Mohimani, H., Babaie-Zadeh, M., Jutten, C.: Estimating the mixing matrix in sparse component analysis (SCA) based on partial k-dimensional subspace clustering. Neurocomputing (Elsevier) 71, 2330–2343 (2008)
Theis, F., Georgiev, P., Cichocki, A.: Robust sparse component analysis based on a generalized hough transform. EURASIP J. Appl. Sig. Process. 2007(1), 86 (2007)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Academic Press, London (2009)
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Boulais, A., Deville, Y., Berné, O. (2017). A Blind Identification and Source Separation Method Based on Subspace Intersections for Hyperspectral Astrophysical Data. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_35
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DOI: https://doi.org/10.1007/978-3-319-53547-0_35
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