A Distributed Adaptive Algorithm for Non-Smooth Spatial Filtering Problems

TL;DR

This paper extends a distributed adaptive algorithm to handle non-smooth spatial filtering problems in wireless sensor networks, enabling regularization techniques like node selection while ensuring convergence.

Contribution

It introduces a convergence-proof extension of the DASF algorithm to non-smooth problems, facilitating regularization and reducing communication costs.

Findings

The non-smooth DASF algorithm converges in static and adaptive scenarios.

Regularizers like node selection are effectively integrated.

Simulations validate the convergence and effectiveness of the extended algorithm.

Abstract

Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive signal fusion (DASF) algorithm solves this problem by having the nodes collaboratively solve low-dimensional versions of the original optimization problem, relying solely on the exchange of compressed views of the sensor data between the nodes. However, the DASF algorithm has only been shown to converge for filtering problems that can be expressed as smooth optimization problems. In this paper, we explore an extension of the DASF algorithm to a family of non-smooth spatial filtering problems, allowing the addition of non-smooth regularizers to the optimization problem, which could for example be used to perform node selection, and eliminate nodes not contributing to the filter objective, therefore further reducing communication costs. We provide a convergence proof of the non-smooth DASF algorithm and validate its convergence via simulations in both a static and adaptive setting.