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When facing graph signal processing tasks, the workhorse assumption is thatthe graph describing the support of the signals is known. However, in manyrelevant applications the available graph suffers from observation errors andperturbations. As a result, any method relying on the graph topology may yieldsuboptimal results if those imperfections are ignored. Motivated by this, wepropose a novel approach for handling perturbations on the links of the graphand apply it to the problem of robust graph filter (GF) identification frominput-output observations. Different from existing works, we formulate anon-convex optimization problem that operates in the vertex domain and jointlyperforms GF identification and graph denoising. As a result, on top of learningthe desired GF, an estimate of the graph is obtained as a byproduct. To handlethe resulting bi-convex problem, we design an algorithm that blends techniquesfrom alternating optimization and majorization minimization, showing itsconvergence to a stationary point. The second part of the paper i) generalizesthe design to a robust setup where several GFs are jointly estimated, and ii)introduces an alternative algorithmic implementation that reduces thecomputational complexity. Finally, the detrimental influence of theperturbations and the benefits resulting from the robust approach arenumerically analyzed over synthetic and real-world datasets, comparing themwith other state-of-the-art alternatives.

Robust Graph Filter Identification and Graph Denoising from Signal Observations