Thermal Source Localization Through Infinite-Dimensional Compressed Sensing

TL;DR

This paper introduces a novel infinite-dimensional compressed sensing approach for thermal source localization, providing theoretical guarantees and demonstrating strong performance in noisy, off-grid, and low-sensor scenarios.

Contribution

It extends the soft recovery framework to noisy measurements and applies it to thermal source localization, with rigorous theoretical analysis and extensive numerical validation.

Findings

Effective in low-sensor scenarios

Robust to high noise levels

Accurate off-grid source positioning

Abstract

We propose a scheme utilizing ideas from infinite dimensional compressed sensing for thermal source localization. Using the soft recovery framework of one of the authors, we provide rigorous theoretical guarantees for the recovery performance. In particular, we extend the framework in order to also include noisy measurements. Further, we conduct numerical experiments, showing that our proposed method has strong performance, in a wide range of settings. These include scenarios with few sensors, off-grid source positioning and high noise levels, both in one and two dimensions.