Sampling And Galerkin Reconstruction In Reproducing Kernel Spaces

Keywords

Finite rate of innovation; Galerkin reconstruction; Iterative approximation-projection algorithm; Oblique projection; Reproducing kernel space; Sampling

Abstract

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 Lp. Also we present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.

Publication Date

9-1-2016

Publication Title

Applied and Computational Harmonic Analysis

Volume

41

Issue

2

Number of Pages

638-659

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.acha.2015.12.007

Socpus ID

84969931541 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84969931541

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