Blind separation of sufficiently sparse sources in multichannel compressed sensing

Abstract

Conventional approaches for blind source separation (BSS) are almost based on the Nyquist sampling theory. Recently, compressed sensing (CS) theory is applied to BSS for the fact that the information of a signal can be preserved in a relatively small number of linear projections. The traditional method for compressive BSS mainly involves two steps: recovering mixed signals from compressed observations and separating source signals from the recovered mixed signals. This paper presents a novel framework for separating and reconstructing the sufficiently sparse sources from compressively sensed linear mixtures simultaneously. Compared with the traditional compressive BSS, the proposed approach can reduce the requirements of sampling speed and operating rate of the devices. Moreover, our approach has better reconstruction results. Simulation results demonstrate the proposed algorithm can separate multichannel sufficiently sparse sources successfully.