Multi-channel Sampling on Graphs and Its Relationship to Graph Filter Banks

TL;DR

This paper introduces a multi-channel sampling framework for graph signals, enabling better recovery of full-band signals beyond traditional bandlimited assumptions, and links it to graph filter banks.

Contribution

It develops a generalized multi-channel sampling approach for graph signals and shows its relation to graph filter banks, enhancing signal recovery methods.

Findings

Effective recovery of full-band graph signals demonstrated

Proposed sampling set selection improves signal reconstruction

Graph filter banks are a special case of the MCS framework

Abstract

In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited one in many applications, such as piecewise constant/smooth and union of bandlimited graph signals. Full-band graph signals can be represented by a mixture of multiple signals conforming to different generation models. This requires the analysis of graph signals via multiple sampling systems, i.e., MCS, while existing approaches only consider single-channel sampling. We develop a MCS framework based on generalized sampling. We also present a sampling set selection (SSS) method for the proposed MCS so that the graph signal is best recovered. Furthermore, we reveal that existing graph filter banks can be viewed as a special case of the proposed MCS. In signal recovery experiments, the proposed method exhibits the effectiveness of recovery for full-band graph signals.