A Pointwise Limit Theorem for Filtered Backprojection in Computed Tomography

Yangbo Ye; Jiehua Zhu; Ge Wang

doi:10.1118/1.1559820

A Pointwise Limit Theorem for Filtered Backprojection in Computed Tomography

Yangbo Ye, Jiehua Zhu, Ge Wang

Mathematical Sciences

University of Iowa

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

Abstract

<div class="line" id="line-5"> Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection&hyphen;based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.</div>

Original language	American English
Journal	Medical Physics
Volume	30
DOIs	https://doi.org/10.1118/1.1559820
State	Published - May 2003

Keywords

Computed tomography
Filtered backprojection
Pointwise limit theorem

DC Disciplines

Mathematics

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Cite this

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title = "A Pointwise Limit Theorem for Filtered Backprojection in Computed Tomography",

abstract = " Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection&hyphen;based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.",

keywords = "Computed tomography, Filtered backprojection, Pointwise limit theorem",

author = "Yangbo Ye and Jiehua Zhu and Ge Wang",

note = "Radiation imaging physics Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Departments of Mathematics, Biomedical Engineering, and Radiology, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Computed tomography (CT) is one of the most important areas in the modern science and technology.",

year = "2003",

month = may,

doi = "10.1118/1.1559820",

language = "American English",

volume = "30",

journal = "Medical Physics",

issn = "0094-2405",

publisher = "John Wiley and Sons Ltd",

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TY - JOUR

T1 - A Pointwise Limit Theorem for Filtered Backprojection in Computed Tomography

AU - Ye, Yangbo

AU - Zhu, Jiehua

AU - Wang, Ge

N1 - Radiation imaging physics Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Departments of Mathematics, Biomedical Engineering, and Radiology, University of Iowa, Iowa City, Iowa 52242 Search for more papers by this author Computed tomography (CT) is one of the most important areas in the modern science and technology.

PY - 2003/5

Y1 - 2003/5

N2 - Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection&hyphen;based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.

AB - Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection&hyphen;based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.

KW - Computed tomography

KW - Filtered backprojection

KW - Pointwise limit theorem

UR - https://doi.org/10.1118/1.1559820

U2 - 10.1118/1.1559820

DO - 10.1118/1.1559820

M3 - Article

SN - 0094-2405

VL - 30

JO - Medical Physics

JF - Medical Physics

ER -

A Pointwise Limit Theorem for Filtered Backprojection in Computed Tomography

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