Tomographic Approach for Sampling Multidimensional Signals with Finite Rate of Innovation

Recently, it was shown that it is possible to sample classes of 1-D and 2-D signal with finite rate of innovation (FRI) [9, 4, 5, 3, 2, 7]. In particular, in [7], we presented local and global schemes for sampling sets of Diracs and bilevel polygons using compactly supported kernels that reproduce polynomials. In sequel to [7], in this paper, we present a Radon transform based hybrid scheme for sampling more general 2-D FRI signals such as piecewise polynomials with polygonal boundaries, and higher dimensional Diracs and bilevel polytopes. The key feature of the proposed scheme is an annihilating-filter-based-back-projection (AFBP) algorithm.