Sampling Set Selection for Graph Signals under Arbitrary Signal Priors

Abstract

We propose a sampling set selection method for graph signals under arbitrary signal priors. Most approaches of graph signal sampling assume that signals are bandlimited. However, in practical situations, there exist many full-band graph signals like piecewise smooth/constant signals. Our sampling set selection method allows for arbitrary graph signal models as long as they are linear. This can be derived from a generalized sampling framework. In contrast to existing works, we focus on the direct sum condition between sampling and reconstruction subspaces where the direct sum condition plays a key role for the best possible recovery of sampled signals. We also design a fast sampling set selection algorithm based on the proposed method with the Neumann series approximation. In sampling and recovery experiments, we validate the effectiveness of the proposed method for several graph signal models.