Chapter 2 Blind Source Separation Based on Dictionary Learning: A Singularity-Aware Approach

Abstract This chapter surveys recent works in applying sparse signal processing techniques, in particular, dictionary learning algorithms to solve the blind source separation problem. For the proof of concepts, the focus is on the scenario where the number of mixtures is not less than that of the sources. Based on the assumption that the sources are sparsely represented by some dictionaries, we present a joint source separation and dictionary learning algorithm (SparseBSS) to separate the noise corrupted mixed sources with very little extra information. We also discuss the singularity issue in the dictionary learning process, which is one major reason for algorithm failure. Finally, two approaches are presented to address the singularity issue. Blind source separation (BSS) has been investigated during the last two decades; many algorithms have been developed and applied in a wide range of applications including biomedical engineering, medical imaging, speech processing, astronomica