Robust blind separation of smooth graph signals using minimization of graph regularized mutual information

Abstract

The smoothness of the graph signals on predefined/constructed graphs appears in many natural applications of processing unstructured (i.e., graph-based) data. In the case of latent sources being smooth graph signals, blind source separation (BSS) quality can be significantly improved by exploiting graph signal smoothness along with the classic measures of statistical independence. In this paper, we propose a BSS method benefiting from the minimization of mutual information as a well-known independence criterion and also graph signal smoothness term of the estimated latent sources, and show that its performance is superior and fairly robust to the state-of-the-art classic and Graph Signal Processing (GSP)-based methods, even in the case of the smooth graph signal sources being heavily corrupted. In addition to the comprehensive complexity and convergence analysis, the asymptotic performance of the proposed method is comprehensively compared with that of the Cramér-Rao Bound (CRB) to illustrate the asymptotic efficiency of the proposed method. Besides, the comprehensive real-world analysis of separating mixed images and speech signals illustrates the applicability and efficiency of the proposed method in real-world scenarios.