Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Lim, Hyeona

Committee Member

Dang, Hai

Committee Member

Yarahmadian, Shantia

Date of Degree

5-12-2023

Document Type

Graduate Thesis - Open Access

Major

Mathematics

Degree Name

Master of Science (M.S.)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of discrepancies between clean and denoised images occur at feature edges, this study examines several convolution-based edge detection methods to isolate relevant feature. The resultant gradient and edge information is used to further parameterize the ��−means non-local method. An additional hybrid method involving the combined contributions of variational and ��−means non-local denoising is proposed, with the weighting determined by edge intensities. This method outperforms the other methods outlined in the study, both conventional and newly presented.

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