Graph-Aware Alternating Minimization for Blind Deconvolution of Graph Filters and Signals

This letter introduces a graph-aware alternating minimization (AM) framework for blind deconvolution of sparse graph signals and low-degree polynomial graph filters. Unlike existing approaches, the proposed method adopts a nonconvex, graph-locality-based strategy to address the ℓ 0 sparsity constraint. At each AM iteration, sparse recovery integrates orthogonal matching pursuit and graph-based branch and bound, and is further refined by a novel multi-support graph correction. This correction improves support estimation by optimizing the generalized information criterion over graph neighborhoods. Filter coefficients are then updated via a spectral least-squares estimator leveraging the graph Fourier representation of polynomial filters. Simulations show that the proposed methods achieve the highest support-recovery F-scores across varying scenarios, while providing a controllable runtime-accuracy tradeoff.