Date of Award
Spring 5-1-2021
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
Recommended Citation
Greenman, Eva Lynn, "Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods" (2021). Dissertations. 1893.
https://aquila.usm.edu/dissertations/1893