Term of Award

Fall 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)


Department of Mathematical Sciences

Committee Chair

Xiezhang Li

Committee Member 1

Jiehua Zhu

Committee Member 2

Yan Wu


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.

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