Honors Theses

Ben Spencer

Affiliation

College of Arts and Sciences, Mathematics and Statistics

College

College of Arts and Sciences

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Department

Department of Mathematics and Statistics

Degree

Bachelor of Science

Degree

Bachelor of Science (B.S.)

Major

Mathematics

Document Type

Immediate Open Access

Abstract

Images occur in many forms in our daily lives, and denoising is one of the most important steps of image analysis in improving the quality of images. It is also used as a preprocessing for other imaging techniques such as feature segmentation and compression. One of the most fundamental mathematical techniques among the various image denoising methods developed for the last two to three decades is using nonlinear partial differential equations from energy minimization. These partial differential equations based methods use the minimizing functional to numerically find the solution. The filtering-based methods using smoothing operators have also been used for image denoising for quite a long time. One of the most remarkable filtering denoising methods is the non-local means filter. This method is non-local since each pixel is denoised using the weighted average of all the pixels in the entire image. It works well for images with repetitive patterns or fine structures. In this thesis, we investigate both methods and test several images to compare their accuracy and efficiency. We also further develop two new methods based on the non-local means filter.

Date Defended

4-23-2021

Thesis Director

Lim, Hyeona

Second Committee Member

McBride, Matthew

Third Committee Member

Oppenheimer, Seth

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