Blind Separation of Orthogonal Mixtures of Spatially-Sparse Sources with Unknown Sparsity Levels and with Temporal Blocks

We address the problem of blind separation of a static, linear orthogonal mixture, where separation is not based on statistical assumptions (such as independence), but on the sources’ spatial sparsity. An algorithm for this problem was proposed by Mishali and Eldar in 2008. It consists of first recovering the supports of the sources, and then recovering their values, but has two shortcomings: One is an assumption that the spatial sparsity level at each time-instant is constant and known; The second is the algorithm’s sensitivity to possible presence of temporal “blocks” of the signals, sharing identical supports. In this work we propose two pre-processing stages for improving the algorithm’s applicability and the performance. A first stage is aimed at identifying “blocks” of similar support, and pruning the data accordingly. A second stage is aimed at recovering the sparsity level at each time-instant. We demonstrate the improvement using both synthetic data and mixed text-images. We also show that the improved algorithm outperforms the recovery rate of alternative source separation methods for such contexts, including K-SVD, a leading method for dictionary learning.