Model-Based Sparse Source Identification

This paper presents a model-based approach for source identification using sparse recovery techniques. In particular, given an arbitrary domain that contains a set of unknown sources and a set of stationary sensors that can measure a quantity generated by the sources, we are interested in predicting the shape, location, and intensity of the sources based on a limited number of sensor measurements. We assume a PDE model describing the steady-state transport of the quantity inside the domain, which we discretize using the Finite Element method (FEM). Since the resulting source identification problem is under-determined for a limited number of sensor measurements and the sought source vector is typically sparse, we employ a novel Reweighted l(1) regularization technique combined with Least Squares Debiasing to obtain a unique, sparse, reconstructed source vector. The simulations confirm the applicability of the presented approach for an Advection-Diffusion problem.