Blind separation of spatially-block-sparse sources from orthogonal mixtures

We addresses the classical problem of blind separation of a static linear mixture, where separation is not based on statistical assumptions (such as independence) regarding the sources, but rather on their spatial (block-) sparsity, and with an additional constraint of an orthogonal mixing-matrix. An algorithm for this problem was recently proposed by Mishali and Eldar, and consists of two steps: one for recovering the support of the sources, and a subsequent one for recovering their values. That algorithm has two shortcomings: One is an assumption that the spatial sparsity level of the sources at each time-instant is constant and known; The second is the algorithm´s sensitivity to the possible presence of temporal “blocks” of the signals with identical support. In this work we propose two pre-processing stages for improving the applicability and the performance of the algorithm. A first stage is aimed at identifying “blocks” of similar support, and pruning the data accordingly for the support-recovery stage. A second stage is aimed at recovering the sparsity level at each time-instant by exploiting observed structural inter-relations between the signals at different time-instants. We demonstrate the improvement over the original algorithm using both synthetic data and mixed text-images. We also show that the algorithm outperforms the recovery rate of alternative source separation methods for such contexts, including K-SVD, a leading method for dictionary learning.