Sampling schemes for 2-D signals with finite rate of innovation using kernels that reproduce polynomials

Abstract

In this paper, we propose new sampling schemes for classes of 2-D signals with finite rate of innovation (FRI). In particular, we consider sets of 2-D Diracs and bilevel polygons. As opposed to using only sine or Gaussian kernels [I. Maravic et al, 2004], we allow the sampling kernel to be any function that reproduces polynomials. In the proposed sampling schemes, we exploit the polynomial approximation properties of the sampling kernels in association with other relevant techniques such as complex-moments [P. Milanfar et al, 1995], annihilating filter method [M. Vetterli et al, 2002], and directional derivatives. Specifically, for the bilevel polygons, we propose two different methods: the first uses a global reconstruction algorithm and complex moments, while the second is based on directional derivatives and local reconstruction algorithms. The trade-off between these two reconstruction modalities is also briefly discussed.