Blind Source Separation based on Compressed Sensing

Abstract

Blind Source Separation (BSS) is an important issue in the coherent processing of multi-dimensional data. To recover and separate the sources from underdetermined mixtures, some prior information like sparse representation is required. The principle is very similar to the new technique named Compressed Sensing (CS), which asserts that one can recover a sparse signal from a limited number of random projections. In this paper, the relationship between BSS and CS is studied by equivalent transformation, then we propose the linear operator by which the relationship between the sources and the mixtures is modeled in two ways: RIP and incoherence, and give some instructive conclusions for the operator design. Numerical simulation applying the FOOMP algorithm and a operator we propose are conducted to demonstrate the good performance of the whole framework.