Mississippi State University
Oppenheimer, Seth F.
Date of Degree
Original embargo terms
MSU Only Indefinitely
Dissertation - Campus Access Only
Doctor of Philosophy
College of Arts and Sciences
Department of Mathematics and Statistics
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.
Bagchi Misra, Arundhati, "Total Variation Based Methods for Speckle Image Denoising" (2012). Theses and Dissertations. 4747.