Interpolation of graph signals using shift-invariant graph filters

Abstract

New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. The schemes are designed within the framework of linear shift-invariant graph filters and consider that the seeding signals are injected only at a subset of interpolating nodes. After several sequential applications of the graph-shift operator - which computes linear combinations of the information available at neighboring nodes - the seeding signals are diffused across the graph and the original bandlimited signal is eventually recovered. Conditions under which the recovery is feasible are given, and the corresponding schemes to recover the signal are proposed. Connections with the classical interpolation in the time domain are also discussed.