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). In particular, in P. Shukla et al., (2005), we presented local and global schemes for sampling sets of Diracs and bilevel polygons using compactly supported kernels that reproduce polynomials. In sequel to P. Shukla et al., (2005), 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.