Dictionary and sparse decomposition method selection for underdetermined blind source separation

In underdetermined BSS problems, it is common practice to exploit the underlying sparsity of the sources. In this work, we propose two approaches to improve the quality and robustness of current algorithms that rely on source sparsity. First, we highlight the benefits of using a matched dictionary as opposed to a standard overcomplete dictionary for separation. Second, we investigate the problem of additive noise for geometric separation methods such as the Hough Transform, and propose using a BESS decomposition algorithm as a robust method for estimating the mixing matrix in the presence of noise. We find that current sparse decomposition methods fail to take advantage of optimal dictionary design and suggest pursuing representations that are less sparse for signal mixtures.