Abstract
We consider the Blind Source Separation problem of linear mixtures with singular matrices and show that it can be solved if the sources are sufficiently sparse. More generally, we consider the problem of identifying the source matrix S ∈ IRnxN if a linear mixture X = AS is known only, where A∈ IRmxn, m ≤ n and the rank of A is less than m. A sufficient condition for solving this problem is that the level of sparsity of S is bigger than m–rank(A) in sense that the number of zeros in each column of S is bigger than m–rank(A). We present algorithms for such identification and illustrate them by examples.
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References
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing. John Wiley, Chichester (2002)
Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)
Eriksson, J., Koivunen, V.: Identifiability and separability of linear ica models revisited. In: Proc. of ICA 2003, pp. 23–27 (2003)
Georgiev, P., Theis, F.J., Cichocki, A.: Blind source separation and sparse component analysis of overcomplete mixtures. In: Proc. of ICASSP 2004, Montreal, Canada (2004)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, Chichester (2001)
Lee, T.-W., Lewicki, M.S., Girolami, M., Sejnowski, T.J.: Blind sourse separation of more sources than mixtures using overcomplete representaitons. IEEE Signal Process. Lett. 6(4), 87–90 (1999)
Theis, F.J., Lang, E.W., Puntonet, C.G.: A geometric algorithm for overcomplete linear ICA. Neurocomputing (2003) (in print)
Waheed, K., Salem, F.: Algebraic Overcomplete Independent Component Analysis. In: Proc. Int. Conf. ICA 2003, Nara, Japan, pp. 1077–1082 (2003)
Zibulevsky, M., Pearlmutter, B.A.: Blind source separation by sparse decomposition in a signal dictionary. Neural Comput. 13(4), 863–882 (2001)
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© 2004 Springer-Verlag Berlin Heidelberg
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Georgiev, P., Theis, F.J. (2004). Blind Source Separation of Linear Mixtures with Singular Matrices. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_16
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DOI: https://doi.org/10.1007/978-3-540-30110-3_16
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