A hierarchical approach for sparse source Blind Signal Separation problem

In this paper, a Blind Signal Separation (BSS) problem is considered: given $X\in {‐{R}}^{m\times N}$ , BSS problem is to find $A\in {‐{R}}^{m\times n}$ and $S\in {‐{R}}^{n\times N}$ , where the matrices are related as X=AS. We have reviewed the sufficient conditions on the structure of X, A and S in terms of sparseness conditions on S, such that the equation $X=\mathit{AS}$ can be solved uniquely (up to permutation and scalability). A hierarchical 0–1 MIP is proposed to solve the problem. Probabilistically, we have shown that every subsequent level of hierarchical MIP will be easier to solve than the precedent level of MIP. Moreover, we have presented case studies that illustrate the performance of proposed solution approach for correlated sparse sources.