Analysis of Source Sparsity and Recoverability for SCA Based Blind Source Separation.

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. [ABSTRACT FROM AUTHOR]