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.Comment: Submitted to the 2024 IEEE International Conference on Acoustics,
Speech, and Signal Processing (ICASSP 2024