Analysis of sparse representation and blind source separation
Neural Computation
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
A Variational Method for Learning Sparse and Overcomplete Representations
Neural Computation
Learning Overcomplete Representations
Neural Computation
Sequential blind extraction of instantaneously mixed sources
IEEE Transactions on Signal Processing
Underdetermined blind source separation based on sparse representation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
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One (of) important application of sparse component analysis (SCA) is in underdetermined blind source separation (BSS). Within a probability framework, this paper focuses on recoverability problem of underdetermined BSS based on a two-stage SCA approach. We consider a general case in which both sources and mixing matrix are randomly drawn. First, we present a recoverability probability estimate under the condition that the nonzero entry number of a source column vector is fixed. Next, we define the sparsity degree of a signal, and establish the relationship between the sparsity degree of sources and recoverability probability. Finally, we explain how to use the relationship to guarantee the performance of BSS. Several simulation results have demonstrated the validity of the probability estimation approach.