Sparse Graph Signal Recovery by the Graph-Based Multiple Generalized Information Criterion (GM-GIC)

This paper investigates the recovery of sparse signals over graphs, which is a common problem in graph signal processing (GSP) applications such as anomaly detection in sensor networks. We represent the sparse graph signals as a graph fil-ter output and pose the problem as hypothesis testing. Based on this representation, we propose the Graph-Based Multiple Generalized Information Criterion (GM-GIC), which leverages the double sparsity of the graph signal and the graph filter. In the first stage of the GM-GIC method, we test each dictionary element (graph filter matrix column) to identify if it captures information on the sparse signal. Next, we partition the subset of informative dictionary elements into smaller subsets that span orthogonal subspaces. Finally, we compute the local GICs over each subset and combine them into a global decision. Simulations show that the GM-GIC method improves the support recovery performance compared with existing methods without significant computational overhead.