Sampling Graph Signals with Sparse Dictionary Representation

Graph sampling strategies require the signal to be relatively sparse in an alternative domain, e.g. bandlimitedness for reconstructing the signal. When such a condition is violated or its approximation demands a large bandwidth, the reconstruction often comes with unsatisfactory results even with large samples. In this paper, we propose an alternative sampling strategy based on a type of overcomplete graph-based dictionary. The dictionary is built from graph filters and has demonstrated excellent sparse representations for graph signals. We recognize the proposed sampling problem as a coupling between support recovery of sparse signals and node selection. Thus, to approach the problem we propose a sampling procedure that alternates between these two. The former estimates the sparse support via orthogonal matching pursuit (OMP), which in turn enables the latter to build the sampling set selection through greedy algorithms. Numerical results corroborate the role of key parameters and the effectiveness of the proposed method.