Low-Bit Quantization of Bandlimited Graph Signals via Iterative Methods

TL;DR

This paper introduces iterative noise-shaping algorithms for low-bit quantization of bandlimited graph signals, leveraging spectral properties and graph incoherence to achieve high-fidelity approximations with theoretical guarantees and extensive empirical validation.

Contribution

It presents novel iterative quantization methods for graph signals that incorporate sampling strategies and theoretical analysis, advancing low-bit graph signal processing.

Findings

High-fidelity approximations with low-bit quantization

Theoretical guarantees for random sampling method

Effective performance demonstrated on synthetic and real-world graphs

Abstract

We study the quantization of real-valued bandlimited signals on graphs, focusing on low-bit representations. We propose iterative noise-shaping algorithms for quantization, including sampling approaches with and without vertex replacement. The methods leverage the spectral properties of the graph Laplacian and exploit graph incoherence to achieve high-fidelity approximations. Theoretical guarantees are provided for the random sampling method, and extensive numerical experiments on synthetic and real-world graphs illustrate the efficiency and robustness of the proposed schemes.