Defense Date

4-15-2004

Graduation Date

Spring 2004

Availability

Immediate Access

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Stacey Levine

Committee Member

Constance D. Ramirez

Committee Member

Eric Rawdon

Committee Member

Kathleen Taylor

Keywords

denoising, image processing, image restoration, inpainting, nonstandard diffusion, optimization

Abstract

Many fields of study use images to make discoveries about the past, decisions for the present and predictions for the future. Images often acquire degradations such as a blur due to a patient moving during an x-ray or noise picked up through remote sensing imaging equipment. Images may also lose information through compression or

transmission. In this thesis, diffusion based models were used to solve the image restoration problem as these models can simultaneously remove noise, preserve edges and restore lost information. Specifically, numerical schemes were developed and tested for denoising via nonstandard diffusion that are more computationally efficient than the current method. Furthermore, a new model for digital inpainting is proposed based on the nonstandard diffusion model. Numerical results illustrate the effectiveness of both the denoising and inpainting models in image restoration.

Format

PDF

Language

English

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