Sampling and Galerkin reconstruction in reproducing kernel spaces

Cheng Cheng; Yingchun Jiang; Qiyu Sun

doi:10.1016/j.acha.2015.12.007

Sampling and Galerkin reconstruction in reproducing kernel spaces

Cheng Cheng, Yingchun Jiang^*, Qiyu Sun

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

10 Citations (Scopus)

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 L^p. Also we present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation. © 2016 Elsevier Inc.

Original language	English
Pages (from-to)	638-659
Journal	Applied and Computational Harmonic Analysis
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/j.acha.2015.12.007
Publication status	Published - 1 Sept 2016
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

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

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title = "Sampling and Galerkin reconstruction in reproducing kernel spaces",

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. {\textcopyright} 2016 Elsevier Inc.",

keywords = "Finite rate of innovation, Galerkin reconstruction, Iterative approximation-projection algorithm, Oblique projection, Reproducing kernel space, Sampling",

author = "Cheng Cheng and Yingchun Jiang and Qiyu Sun",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "2016",

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doi = "10.1016/j.acha.2015.12.007",

language = "English",

volume = "41",

pages = "638--659",

journal = "Applied and Computational Harmonic Analysis",

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TY - JOUR

T1 - Sampling and Galerkin reconstruction in reproducing kernel spaces

AU - Cheng, Cheng

AU - Jiang, Yingchun

AU - Sun, Qiyu

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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. © 2016 Elsevier Inc.

AB - 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. © 2016 Elsevier Inc.

KW - Finite rate of innovation

KW - Galerkin reconstruction

KW - Iterative approximation-projection algorithm

KW - Oblique projection

KW - Reproducing kernel space

KW - Sampling

UR - http://www.scopus.com/inward/record.url?scp=84969931541&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84969931541&origin=recordpage

U2 - 10.1016/j.acha.2015.12.007

DO - 10.1016/j.acha.2015.12.007

M3 - RGC 21 - Publication in refereed journal

SN - 1063-5203

VL - 41

SP - 638

EP - 659

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

Sampling and Galerkin reconstruction in reproducing kernel spaces

Abstract

Bibliographical note

Research Keywords

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