Distributed Signal Processing via Chebyshev Polynomial Approximation

TL;DR

This paper introduces a distributed signal processing method on graphs using Chebyshev polynomial approximations, enabling efficient and scalable operations like smoothing and classification across large networks.

Contribution

The paper proposes a novel distributed approach leveraging Chebyshev polynomial approximations for graph signal processing, improving scalability and efficiency.

Findings

Communication requirements scale gracefully with network size

Effective for smoothing, denoising, inverse filtering, and classification

Demonstrates practical applicability in distributed graph signal processing

Abstract

Unions of graph multiplier operators 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. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be applied to distributed processing tasks such as smoothing, denoising, inverse filtering, and semi-supervised classification, and show that the communication requirements of the method scale gracefully with the size of the network.