Thermal Source Localization Through Infinite-Dimensional Compressed Sensing
This work addresses the problem of localizing thermal sources from limited sensor data, offering a theoretically grounded approach that handles noise and off-grid sources.
The paper proposes a compressed sensing-based method for thermal source localization, providing theoretical guarantees for recovery with noisy measurements and demonstrating strong performance in numerical experiments across various challenging settings.
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.