Date of Award

Spring 5-5-2021

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

School

Mathematics and Natural Sciences

Committee Chair

Dr. James V. Lambers, Committee Chair

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

Dr. Jiu Ding

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Dr. Haiyan Tian

Committee Member 3 School

Mathematics and Natural Sciences

Committee Member 4

Dr. Huiqing Zhu

Committee Member 4 School

Mathematics and Natural Sciences

Abstract

The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in Perona-Malik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning edge detector parameters so as to not require human interaction, we propose to automatically adapt the parameters to specific images. It is anticipated that with KSS methods, in conjunction with efficient block processing, we will set new standards for efficiency and automation.

ORCID ID

0000-0002-7591-5657

Share

COinS