Blind separation of sparse sources from nonlinear mixtures

Abstract

Blind source separation (BSS) has been studied well when the sources are sparse signals and their combinations are linear. Sparse component analysis (SCA) or dictionary learning algorithms propose well-known approaches for performing BSS in this model. In this study, we explore BSS when the sources are sparse signals, however, their combinations are nonlinear. The considered scenario can be adapted to several signal processing applications such as machine learning and system identification. To perform BSS, we first approximate the nonlinear mixture functions with the polynomial functions. Then, using an alternating approach, we estimate the sources and the coefficients of polynomial functions. The considered strategy is similar to one employed in dictionary learning algorithms for sparse representation of signals. In fact, in iterations where the sources are estimated, we cluster the signals, and in iterations where the coefficients of polynomial functions are estimated, we assign a polynomial manifold to each cluster. The identifiability issues of the considered nonlinear model are also discussed. Experimental results demonstrate the effectiveness of the proposed method relative to state-of-the-art methods.