  When approaching graph signal processing tasks, graphs are usually assumed to
be perfectly known. However, in many practical applications, the observed
(inferred) network is prone to perturbations which, if ignored, will hinder
performance. Tailored to those setups, this paper presents a robust formulation
for the problem of graph-filter identification from input-output observations.
Different from existing works, our approach consists in addressing the robust
identification by formulating a joint graph denoising and graph-filter
identification problem. Such a problem is formulated as a non-convex
optimization, suitable relaxations are proposed, and graph-stationarity
assumptions are incorporated to enhance performance. Finally, numerical
experiments with synthetic and real-world graphs are used to assess the
proposed schemes and compare them with existing (robust) alternatives.
