Graph Signal Processing Meets Blind Source Separation

TL;DR

This paper advances blind source separation for graph signals by developing new methods that leverage graph structure and non-Gaussianity, providing theoretical bounds and demonstrating improved efficiency in separating signals.

Contribution

It introduces a nonparametric BSS method aligned with GSP, derives the CRB for Gaussian graph signals, and proposes two methods for non-Gaussian signals with enhanced robustness.

Findings

Derived the CRB for Gaussian moving average graph signals.

Proposed two new BSS methods for non-Gaussian graph signals.

Numerical results show improved separation efficiency.

Abstract

In graph signal processing (GSP), prior information on the dependencies in the signal is collected in a graph which is then used when processing or analyzing the signal. Blind source separation (BSS) techniques have been developed and analyzed in different domains, but for graph signals the research on BSS is still in its infancy. In this paper, this gap is filled with two contributions. First, a nonparametric BSS method, which is relevant to the GSP framework, is refined, the Cram\'{e}r-Rao bound (CRB) for mixing and unmixing matrix estimators in the case of Gaussian moving average graph signals is derived, and for studying the achievability of the CRB, a new parametric method for BSS of Gaussian moving average graph signals is introduced. Second, we also consider BSS of non-Gaussian graph signals and two methods are proposed. Identifiability conditions show that utilizing both graph structure and non-Gaussianity provides a more robust approach than methods which are based on only either graph dependencies or non-Gaussianity. It is also demonstrated by numerical study that the proposed methods are more efficient in separating non-Gaussian graph signals.