Sampling of graph signals: Successive local aggregations at a single node

Abstract

A new scheme to sample bandlimited graph signals is proposed. The signals are defined in the nodes of a graph and admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so- called graph-shift operator. Most of the existing works focused on using the value of the signal observed at a subset of nodes to recover the signal in the entire graph. Differently, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-shift operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle, which is the support of time-varying signals, our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, which plays a critical role in guaranteeing recovery when sampling time-varying signals, is preserved.