Term of Award
Fall 2014
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Xiezhang Li
Committee Member 1
Jiehua Zhu
Committee Member 2
Yan Wu
Abstract
Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step size so that the total variation is minimized. A new minimization problem is also proposed. Numerical tests are included to illustrate the improvement.
OCLC Number
929065757
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9915984088302950
Recommended Citation
Yeboah, Anna N., "Selection of Step Size for Total Variation Minimization in CT" (2014). Electronic Theses and Dissertations. 1179.
https://digitalcommons.georgiasouthern.edu/etd/1179
Research Data and Supplementary Material
No
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons
