Preconditioned Gradient Descent Algorithm for Inverse Filtering on Spatially Distributed Networks

TL;DR

This paper introduces a preconditioned gradient descent algorithm for inverse filtering on spatially distributed networks, addressing implementation challenges with limited-capacity agents and confined communication ranges.

Contribution

It proposes a novel, exponentially convergent algorithm suitable for vertex-level implementation and time-varying inverse filtering on SDNs with small geodesic-width.

Findings

Algorithm converges exponentially

Applicable to time-varying inverse filtering

Operates at vertex level in SDNs

Abstract

Graph filters and their inverses have been widely used in denoising, smoothing, sampling, interpolating and learning. Implementation of an inverse filtering procedure on spatially distributed networks (SDNs) is a remarkable challenge, as each agent on an SDN is equipped with a data processing subsystem with limited capacity and a communication subsystem with confined range due to engineering limitations. In this letter, we introduce a preconditioned gradient descent algorithm to implement the inverse filtering procedure associated with a graph filter having small geodesic-width. The proposed algorithm converges exponentially, and it can be implemented at vertex level and applied to time-varying inverse filtering on SDNs.