Heuristics for Efficient Sparse Blind Source Separation

In the BSS [1] framework, the data are composed of m observations, eachof which has t samples. These observations are supposed to be some linear combinations of n sources. The objective of BSS is to retrieve the sources as well as the mixing coefficients. In matrix form, the goal is therefore to find two matrices S (of size n t) and A (of size m n), called respectively the source and the mixing matrices, such that: X AS N, whereX (of sizem t) is the observation matrix that is corrupted with some unkwown noiseN. Since it requires tackling an ill-posed unsupervised matrix factorization problem, further assumptions are needed, including the statistical independanceof the sources (ICA - [1]), the non-negativity of A and S [2]. In this work, we will focus on the sparsity of the sources [3, 4, 5, 6].