Sampling and Galerkin reconstruction in reproducing kernel spaces

In this paper, we introduce a fidelity measure depending on a given sampling scheme and we propose a Galerkin method in Banach space setting for signal reconstruction. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm in a reproducing kernel subspace of LpLp. Also we present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.