A New Approach of Blind Channel Identification in Frequency Domain
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Underdetermined Blind Source Separation Using SVM
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Source localization using a sparse representation framework to achieve superresolution
Multidimensional Systems and Signal Processing
Two conditions for equivalence of 0-norm solution and 1-norm solution in sparse representation
IEEE Transactions on Neural Networks
Speech emotion recognition system based on L1 regularized linear regression and decision fusion
ACII'11 Proceedings of the 4th international conference on Affective computing and intelligent interaction - Volume Part II
Maximum contrast analysis for nonnegative blind source separation
Computers & Mathematics with Applications
Analysis of source sparsity and recoverability for SCA based blind source separation
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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An important application of sparse representation is underdetermined blind source separation (BSS), where the number of sources is greater than the number of observations. Within the stochastic framework, this paper discusses recoverability of underdetermined BSS based on a two-stage sparse representation approach. The two-stage approach is effective when the source matrix is sufficiently sparse. The first stage of the two-stage approach is to estimate the mixing matrix, and the second is to estimate the source matrix by minimizing the 1-norms of the source vectors subject to some constraints. After estimating the mixing matrix and fixing the number of nonzero entries of a source vector, we estimate the recoverability probability (i.e., the probability that the source vector can be recovered). A general case is then considered where the number of nonzero entries of the source vector is fixed and the mixing matrix is drawn from a specific probability distribution. The corresponding probability estimate on recoverability is also obtained. Based on this result, we further estimate the recoverability probability when the sources are also drawn from a distribution (e.g., Laplacian distribution). These probability estimates not only reflect the relationship between the recoverability and sparseness of sources, but also indicate the overall performance and confidence of the two-stage sparse representation approach for solving BSS problems. Several simulation results have demonstrated the validity of the probability estimation approach.