3D reconstruction of wave-propagated point sources from boundary measurements using joint sparsity and finite rate of innovation

Reconstruction of point sources from boundary measurements is a challenging problem in many applications. Recently, we proposed a new sensing and non-iterative reconstruction scheme for systems governed by the three-dimensional wave equation. The points sources are described by their magnitudes and positions. The core of the method relies on the principles of finite-rate-of-innovation, and allows retrieving the parameters in the continuous domain without discretization. Here we extend the method when the source configuration shows joint sparsity for different temporal frequencies; i.e., the sources have same positions for different frequencies, not necessarily the same magnitudes. We demonstrate that joint sparsity improves upon the robustness of the estimation results. In addition, we propose a modified multi-source version of Dijkstra´s algorithm to recover the Z parameters. We illustrate the feasibility of our method to reconstruct multiple sources in a 3-D spherical geometry.