On reconstruction from non-uniform spectral data

Adityavikram Viswanathan; Anne Gelb; Douglas Cochran; Rosemary Renaut

doi:10.1007/s10915-010-9364-3

On reconstruction from non-uniform spectral data

Adityavikram Viswanathan, Anne Gelb, Douglas Cochran, Rosemary Renaut

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.

Original language	English (US)
Pages (from-to)	487-513
Number of pages	27
Journal	Journal of Scientific Computing
Volume	45
Issue number	1-3
DOIs	https://doi.org/10.1007/s10915-010-9364-3
State	Published - Oct 2010

Keywords

Convolutional gridding
Non-harmonic Fourier reconstruction
Sampling density
Spectral re-projection

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-010-9364-3

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title = "On reconstruction from non-uniform spectral data",

abstract = "This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.",

keywords = "Convolutional gridding, Non-harmonic Fourier reconstruction, Sampling density, Spectral re-projection",

author = "Adityavikram Viswanathan and Anne Gelb and Douglas Cochran and Rosemary Renaut",

note = "Funding Information: Acknowledgements This work was supported in part by National Science Foundation grants DMS 0510813 and FRG 0652833.",

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AU - Viswanathan, Adityavikram

AU - Gelb, Anne

AU - Cochran, Douglas

AU - Renaut, Rosemary

N1 - Funding Information: Acknowledgements This work was supported in part by National Science Foundation grants DMS 0510813 and FRG 0652833.

PY - 2010/10

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AB - This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.

KW - Convolutional gridding

KW - Non-harmonic Fourier reconstruction

KW - Sampling density

KW - Spectral re-projection

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EP - 513

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1-3

ER -

On reconstruction from non-uniform spectral data

Abstract

Keywords

ASJC Scopus subject areas

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