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Inversion of the star transform.
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View online- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Zhao, Fan, author.
- Language:
- English
- Subjects (All):
- Applied mathematics.
- Computer science.
- Applied Mathematics and Computational Science--Penn dissertations.
- Penn dissertations--Applied Mathematics and Computational Science.
- Local Subjects:
- Applied mathematics.
- Computer science.
- Applied Mathematics and Computational Science--Penn dissertations.
- Penn dissertations--Applied Mathematics and Computational Science.
- Genre:
- Academic theses.
- Physical Description:
- 1 online resource (96 pages)
- Contained In:
- Dissertation Abstracts International 76-05B(E).
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor, MI : ProQuest, 2014.
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- We define the star transform as a generalization of the broken ray transform for image reconstruction in single scattering tomography. Using the star transform provides advantages including possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously. We derive the star transform from physical principles, and derive several computationally efficient algorithms for its inversion. We discuss mathematical properties and analyze numerical stability of inversion, and obtain necessary conditions for stable reconstruction. An approach combining scattered rays and ballistic rays to improve reconstruction is provided, and total variation and L1 regularization are utilized to remove noise. Numerical experiments are carried out to test the algorithms of inversion, the possibility to recover the absorption and the scattering coefficients, and the effect of different regularizations.
- Notes:
- Source: Dissertation Abstracts International, Volume: 76-05(E), Section: B.
- Adviser: Vadim A. Markel.
- Department: Applied Mathematics and Computational Science.
- Thesis Ph.D. University of Pennsylvania 2014.
- Local Notes:
- School code: 0175.
- ISBN:
- 9781321480535
- Access Restriction:
- Restricted for use by site license.
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