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Curvelets and the Radon Transform

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Date Issued:
2013
Abstract/Description:
Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated Radon data problems. As a result, using a curvelet representation to invert radon data allows the chance of higher quality images to be produced. This paper examines this method of reconstruction for computed tomography (CT). A brief history of CT, an introduction to the theory behind the method, and implementation details will be provided.
Title: Curvelets and the Radon Transform.
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Name(s): Dickerson, Jill, Author
Katsevich, Alexander, Committee Chair
Tamasan, Alexandru, Committee Member
Moore, Brian, Committee Member
, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2013
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated Radon data problems. As a result, using a curvelet representation to invert radon data allows the chance of higher quality images to be produced. This paper examines this method of reconstruction for computed tomography (CT). A brief history of CT, an introduction to the theory behind the method, and implementation details will be provided.
Identifier: CFE0004674 (IID), ucf:49852 (fedora)
Note(s): 2013-05-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Curvelet -- Radon transform -- image reconstruction -- computed tomography
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0004674
Restrictions on Access: public 2013-05-15
Host Institution: UCF

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