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Blind deconvolution over graphs involves using (observed) output graphsignals to obtain both the inputs (sources) as well as the filter that drives(models) the graph diffusion process. This is an ill-posed problem thatrequires additional assumptions, such as the sources being sparse, to besolvable. This paper addresses the blind deconvolution problem in the presenceof imperfect graph information, where the observed graph is a perturbed versionof the (unknown) true graph. While not having perfect knowledge of the graph isarguably more the norm than the exception, the body of literature on this topicis relatively small. This is partly due to the fact that translating theuncertainty about the graph topology to standard graph signal processing tools(e.g. eigenvectors or polynomials of the graph) is a challenging endeavor. Toaddress this limitation, we propose an optimization-based estimator that solvesthe blind identification in the vertex domain, aims at estimating the inverseof the generating filter, and accounts explicitly for additive graphperturbations. Preliminary numerical experiments showcase the effectiveness andpotential of the proposed algorithm.

Blind Deconvolution of Sparse Graph Signals in the Presence of Perturbations