Abstract
Blind source separation has found applications in various areas including biomedical signal processing and genomic signal processing. Often, blind source separation is performed via independent component analysis (ICA) under the assumption of mutual independence among source signals. However, in bio-signal and genomic signal processing, the assumption of independence is often untrue, and the performance of the ICA approach is not so good. Much effort has been devoted to searching alternative approaches to blind source separation without the independence assumption. In this paper we present a sparse component analysis method, which exploits the sparseness of the source signals and makes the separated signals as sparse as possible according to a properly defined sparsity function, to reliably extract source signals from their mixtures. Some related theoretical and practical issues are investigated, with support and validation by simulation results.
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References
Jutten, C., Herault, J.: Blind separation of sources, part i: An adaptive algorithm based on neuromimetic architechture. Signal Processing 24, 1–10 (1991)
Kagan, A.M., Linnik, J.V., Rao, C.R.: Characterization problems in Mathematical Statistics. Wiley, Chichester (1973)
Comon, P.: Independent component analysis, a new concept. Signal Processing 36, 287–314 (1994)
Lee, S.I., Batzoglou, S.: Application of independent component analysis to microarrays. Genome Biology 4 (2003) (Art.R76)
Ren, J.Y., Chang, C.Q., Fung, P.C.W., Shen, J.G., Chan, F.H.Y.: Free radical EPR spectroscopy analysis using blind source separation. Journal of Magnetic esonance 166, 82–91 (2004)
Chang, C.Q., Yau, S.F., Kwok, P., Chan, F.H.Y., Lam, F.K.: Uncorrelated component analysis for blind source separation. Circuits Systems and Signal Processing 18, 225–239 (1999)
Tong, L., Liu, R.W., Soon, V., Huang, Y.F.: Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems 38, 499–509 (1991)
Chang, C.Q., Ding, Z., Yau, S.F., Chan, F.H.Y.: A matrix-pencil approach to blind separation of colored nonstationary signals. IEEE Transactions on Signal Processing 48, 900–907 (2000)
Tang, A.C., Liu, J.Y., Sutherland, M.T.: Recovery of correlated neuronal sources from EEG: The good and bad ways of using SOBI. NeuroImage 28(2), 507–519 (2005)
Ting, K.H., Fung, P.C.W., Chang, C.Q., Chan, F.H.Y.: Automatic correction of artifact from single-trial event related potentials by blind source separation using second order statistics only. Medical Engineering & Physics (2006) (in press)
Lee, D.D., Seung, H.S.: Learning the parts of objects with non-negative matrix factorization. Nature 405(6755), 788–791 (1999)
Donoho, D., Stodden, V.: When does non-negative matrix factorization give a correct decomposition into parts? In: Advances in Neural Information Processing 16 (Proc. NIPS 2003). MIT Press, Cambridge (2004)
Plumbley, M.D.: Algorithms for non-negative independent component analysis. IEEE Trans. on Neural Network 14, 534–543 (2003)
O’Grady, P.D., Pearlmutter, B.A., Rickard, S.T.: Survey of sparse and non-sparse methods in source separation. International Journal of Imaging Systems and Technology 15(1), 18–33 (2005)
Georgiev, P., Theis, F., Cichocki, A.: Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans. on Neural Networks 16(4), 992–996 (2005)
Chang, C.Q., Ren, J.Y., Fung, P.C.W., Chan, F.H.Y.: A sparse component analysis approach to EPR spectra decomposition. In: Proc. Int. Symp. on Nonlinear Theory and its Applications (NOLTA 2004), Fukuoka, Japan (2004)
Chang, C.Q., Ren, J.Y., Fung, P.C.W., Hung, Y.S., Shen, J.G., Chan, F.H.Y.: Novel sparse component analysis approach to free radical EPR spectra decomposition. Journal of Magnetic Resonance 175, 242–255 (2005)
Li, Y., Cichocki, A., Amari, S.: Analysis of sparse representation and blind source separation. Neural Computation 16(6), 1193–1234 (2004)
Donoho, D., Elad, M.: Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization. Proc. Nat. Acad. Sci. USA 100(5), 2197–2202 (2003)
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Chang, C., Fung, P.C.W., Hung, Y.S. (2006). On a Sparse Component Analysis Approach to Blind Source Separation. In: Rosca, J., Erdogmus, D., PrÃncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_95
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DOI: https://doi.org/10.1007/11679363_95
Publisher Name: Springer, Berlin, Heidelberg
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