Recovery of Graph Signals from Sign Measurements

TL;DR

This paper addresses the challenge of reconstructing band-limited graph signals using only sign measurements, proposing a greedy sampling strategy and validating its effectiveness through simulations.

Contribution

It introduces a novel greedy sampling method for recovering graph signals from sign measurements, extending traditional sampling techniques to non-continuous data.

Findings

The greedy sampling algorithm outperforms random sampling in signal reconstruction accuracy.

Simulation results confirm the effectiveness of the proposed approach.

The method is applicable to scenarios with limited or sign-only observations.

Abstract

Sampling and interpolation have been extensively studied, in order to reconstruct or estimate the entire graph signal from the signal values on a subset of vertexes, of which most achievements are about continuous signals. While in a lot of signal processing tasks, signals are not fully observed, and only the signs of signals are available, for example a rating system may only provide several simple options. In this paper, the reconstruction of band-limited graph signals based on sign sampling is discussed and a greedy sampling strategy is proposed. The simulation experiments are presented, and the greedy sampling algorithm is compared with random sampling algorithm, which verify the validity of the proposed approach.