Underdetermined Blind Source Separation Using Sparse Coding

In an underdetermined mixture system with n unknown sources, it is a challenging task to separate these sources from their m observed mixture signals, where m . n. By exploiting the technique of sparse coding, we propose an effective approach to discover some 1-D subspaces from the set consisting of all the time-frequency (TF) representation vectors of observed mixture signals. We show that these 1-D subspaces are associated with TF points where only single source possesses dominant energy. By grouping the vectors in these subspaces via hierarchical clustering algorithm, we obtain the estimation of the mixing matrix. Finally, the source signals could be recovered by solving a series of least squares problems. Since the sparse coding strategy considers the linear representation relations among all the TF representation vectors of mixing signals, the proposed algorithm can provide an accurate estimation of the mixing matrix and is robust to the noises compared with the existing underdetermined blind source separation approaches. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.

I. Introduction

Blind source separation (BSS) aims at separating the original source signals from their mixtures without any a priori knowledge about the mixing matrix and the source signals [1]–[3]. BSS has attracted considerable research attentions because of its wide applications in biomedical engineering, remote sensing, speech recognition, and communication systems [4]. A large number of BSS algorithms have been developed in the past decades, and most of them assume that the number of sensors is not less than the number of sources. In practice, however, this assumption is difficult to be satisfied. For example, in a wireless sensor network, the number of sources is sometimes unknown to the receivers. Thus, the number of the disposed receivers could be less than the number of the sources, which leads to a more challenging problem, i.e., underdetermined BSS (UBSS) [5]–[13].