Blind Deconvolution of Graph Signals: Robustness to Graph Perturbations

TL;DR

This paper introduces a robust method for blind deconvolution of graph signals that remains effective despite small perturbations in the underlying graph structure, using a linear programming approach and eigenbasis denoising.

Contribution

It provides stable recovery conditions and a convergent algorithm for blind deconvolution on perturbed graphs, extending prior work that assumed perfect eigenbasis knowledge.

Findings

Algorithm demonstrates robustness in numerical tests.

Stable recovery conditions are established for perturbed graphs.

Proposed method outperforms existing approaches under graph perturbations.

Abstract

We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter invertibility requirement along with input sparsity allow for an efficient linear programming reformulation. Unlike prior art that relied on perfect knowledge of the graph eigenbasis, here we derive stable recovery conditions in the presence of small graph perturbations. We also contribute a provably convergent robust algorithm, which alternates between blind deconvolution of graph signals and eigenbasis denoising in the Stiefel manifold. Reproducible numerical tests showcase the algorithm's robustness under several graph eigenbasis perturbation models.