Selection of Step Size for Total Variation Minimization in CT

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Yeboah, Anna N

Contributors dc:contributor

• Jiehua Zhu
• Yan Wu

• ETD
• Total Variation Minimization
• Compressive Sampling
• L1 Minimization
• Step Size
• Computed Tomography
• Numerical Analysis and Computation
• Numerical Analysis and Scientific Computing

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1179

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2233