Blind Deconvolution of Sparse Graph Signals in the Presence of Perturbations

TL;DR

This paper introduces an optimization-based method for blind deconvolution of sparse graph signals that accounts for graph perturbations, improving source and filter estimation under uncertain graph topology.

Contribution

It proposes a novel estimator that explicitly models additive graph perturbations in blind deconvolution, addressing a gap in handling imperfect graph information.

Findings

The proposed algorithm effectively estimates sources and filters despite graph perturbations.

Numerical experiments demonstrate the method's potential and robustness.

The approach advances blind deconvolution techniques in realistic, uncertain graph scenarios.

Abstract

Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional assumptions, such as the sources being sparse, to be solvable. This paper addresses the blind deconvolution problem in the presence of imperfect graph information, where the observed graph is a perturbed version of the (unknown) true graph. While not having perfect knowledge of the graph is arguably more the norm than the exception, the body of literature on this topic is relatively small. This is partly due to the fact that translating the uncertainty about the graph topology to standard graph signal processing tools (e.g. eigenvectors or polynomials of the graph) is a challenging endeavor. To address this limitation, we propose an optimization-based estimator that solves the blind identification in the vertex domain, aims at estimating the inverse of the generating filter, and accounts explicitly for additive graph perturbations. Preliminary numerical experiments showcase the effectiveness and potential of the proposed algorithm.