Sampling and Galerkin reconstruction in reproducing kernel spaces

Abstract

In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. 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. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.

References in corpus (2)

• Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
• On stable reconstructions from nonuniform Fourier measurements

Cited by in corpus (1)

• Spatially Distributed Sampling and Reconstruction