Approximate Recovery of Initial Point-like and Instantaneous Sources from Coarsely Sampled Thermal Fields via Infinite-Dimensional Compressed Sensing

Axel Flinth, Ali Hashemi

Abstract: We propose a method for resolving the positions of the initial source of heat propagation fields. The method relies on the recent theory of compressed sensing off the grid, i.e. TV- minimization. Based on the so-called soft recovery framework, we are able to derive rigorous theoretical guarantees of approximate recovery of the positions. Numerical experiments show a satisfactory performance of our method.