Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Lim, Hyeona

Committee Member

Kim, Seongjai

Committee Member

Oppenheimer, Seth F.

Committee Member

Yarahmadian, Shantia

Committee Member

Xu, Xiangsheng

Date of Degree

8-11-2012

Original embargo terms

MSU Only Indefinitely

Document Type

Dissertation - Campus Access Only

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

This dissertation is about the partial differential equation (PDE) based image denoising models. In particular, we are interested about speckle noise images. We provide the mathematical analysis of existing speckle denoising models and propose three new models based on total variation minimization methods. The first model is developed using a new speckle noise model and the solution of associated numerical scheme is proven to be stable. The second one is a speckle version of Chambolle algorithm and the convergence of the numerical solution was proved under certain assumptions. The final model is a nonlocal PDE based speckle denoising model derived by combining the excellent noise removal properties of the nonlocal means algorithm with the PDE models. We enhanced the computational efficiency of this model by adopting the Split Bregman method. Numerical results of all three models show that they compare favorably to the conventional models.

URI

https://hdl.handle.net/11668/20134

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