Chebyshev Polynomial Approximation for Distributed Signal Processing

TL;DR

This paper introduces a distributed method for applying graph Fourier multipliers using Chebyshev polynomial approximations, enabling efficient processing of high-dimensional signals in sensor networks with scalable communication costs.

Contribution

It presents a novel Chebyshev polynomial-based approximation technique for distributed implementation of graph Fourier multipliers, improving efficiency and scalability.

Findings

Effective distributed denoising demonstrated

Communication costs scale gracefully with network size

Method enables efficient high-dimensional signal processing

Abstract

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.