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...

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Vydáno v:Applied and computational harmonic analysis Ročník 41; číslo 2; s. 638 - 659
Hlavní autoři: Cheng, Cheng, Jiang, Yingchun, Sun, Qiyu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.09.2016
Témata:
Finite rate of innovation
Galerkin reconstruction
Iterative approximation-projection algorithm
Oblique projection
Reproducing kernel space
Sampling
Oblique projection
46E22
Galerkin reconstruction
Iterative approximation-projection algorithm
65J22
Reproducing kernel space
Sampling
94A20
Finite rate of innovation
ISSN:1063-5203, 1096-603X
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Popis
Shrnutí: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.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2015.12.007