DESIGN OF SAMPLING KERNELS AND SAMPLING RATES FOR TWO-DIMENSIONAL FINITE RATE OF INNOVATION SIGNALS

This paper focuses on the design of sampling kernels and critical sampling rates for reconstruction of two-dimensional finite-rate-of-innovation (2D-FRI) signals from their samples. A class of aperiodic 2D sum-of-modulated-splines (2D-SMS) sampling kernels and sampling rates lower than the other state-of-the-art techniques are proposed. The 2D kernels proposed do not require a periodization to handle aperiodic signals. The proposed design also allows for reduced computation complexity. The reconstruction proceeds using the standard FRI reconstruction machinery. We demonstrate successful recovery using signals that are a sum of 2D Gaussians. The reconstruction performance of various members of the proposed family of kernels is evaluated through Monte Carlo simulations and compared against the Cramer-Rao lower bound (CRLB) for various noise levels