On Random Sampling of Diffused Graph Signals with Sparse Inputs on Vertex Domain

TL;DR

This paper analyzes the conditions for successful random sampling and recovery of non-smooth, diffused sparse graph signals, introducing an adaptive sampling strategy and validating results through simulations.

Contribution

It provides a theoretical framework for sampling diffused sparse graph signals, including explicit sampling bounds and an adaptive strategy for improved performance.

Findings

Theoretical bounds for sampling sparse diffused graph signals.

Explicit sampling number estimates for binary graph models.

Adaptive variable-density sampling outperforms uniform sampling.

Abstract

The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth graph signals, few research has been devoted to non-smooth graph signals, especially to sparse graph signals, which are also of importance in many practical applications. This paper addresses the random sampling of non-smooth graph signals generated by diffusion of sparse inputs. We aim to present a solid theoretical analysis on the random sampling of diffused sparse graph signals, which can be parallel to that of band-limited graph signals, and thus present a sufficient condition to the number of samples ensuring the unique recovery for uniform random sampling. Then, we focus on two classes of widely used binary graph models, and give explicit and tighter estimations on the sampling numbers ensuring unique recovery. We also propose an adaptive variable-density sampling strategy to provide a better performance than uniform random sampling. Finally, simulation experiments are presented to validate the effectiveness of the theoretical results.