BLIND SOURCE SEPARATION USING COMPRESSED SENSING FRAMEWORK

Abstract

Sparse recovery is the problem of reconstructing a sparse signal, which satisfies a linear system of equations, from the observed data and the measurement matrix. Even though it is a poorly defined problem, under certain conditions, a solution exhibiting uniqueness, stability and computational practicability can be obtained. Some of the sparse recovery algorithms are discussed in this work. Sparse signal reconstruction finds its application fields of Compressive Sensing and Blind Source Separation. Compressive Sensing is a rapidly growing field in signal processing in which data is directly collected in the compressed form by sampling the signal at sub-Nyquist rates. Blind Source Separation has attracted a great deal of attention over the last few years and deals with the important issue of recovering signals from an undetermined linear combination without any information about the source signals and the mixing procedure. The similarity between compressive sensing and blind source separation is discussed. Following this the blind source separation problem is modelled as a compressive sensing problem and separation of signals is achieved from a compressed mixture using CS-BSS.