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On the range of the Attenuated Radon Transform in strictly convex sets.

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Date Issued:
2014
Abstract/Description:
In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field.
Title: On the range of the Attenuated Radon Transform in strictly convex sets.
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Name(s): Sadiq, Kamran, Author
Tamasan, Alexandru, Committee Chair
Nashed, M, Committee Member
Katsevich, Alexander, Committee Member
Dogariu, Aristide, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2014
Publisher: University of Central Florida
Language(s): English
Abstract/Description: In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field.
Identifier: CFE0005408 (IID), ucf:50437 (fedora)
Note(s): 2014-08-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): Attenuated Radon Transform -- A-analytic maps -- Hilbert Transform -- Attenuated Doppler transform.
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005408
Restrictions on Access: public 2014-08-15
Host Institution: UCF

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