Extension of SoS sampling kernels for 2D FRI problems

The problem of sampling a 2D Poisson process is considered. Recently, such problems have been denoted as sampling of signals with finite rate of innovation. Therefore, a well-known sampling approach for the 1D approach is extended to the 2D case and the theoretic sampling bounds as well as the reconstruction approach are shown. By providing results from numerical simulations it can be demonstrated that reconstruction is exact up to numerical precision.