Efficient Denoising and Sharpening of Color Images through Numerical Solution of Nonlinear Diffusion Equations

Author

Linh T. Duong, University of Southern Mississippi

Date of Award

Spring 5-2017

Degree Type

Honors College Thesis

Department

Mathematics

First Advisor

James V. Lambers

Advisor Department

Mathematics

Abstract

The purpose of this project is to enhance color images through denoising and sharpening, two important branches of image processing, by mathematically modeling the images. Modifications are made to two existing nonlinear diffusion image processing models to adapt them to color images. This is done by treating the red, green, and blue (RGB) channels of color images independently, contrary to the conventional idea that the channels should not be treated independently. A new numerical method is needed to solve our models for high resolution images since current methods are impractical. To produce an efficient method, the solution is represented as a linear combination of sines and cosines for easier numerical treatment and then computed by a combination of Krylov subspace spectral (KSS) methods and exponential propagation iterative (EPI) methods. Numerical experiments demonstrate that the proposed approach for image processing is effective for denoising and sharpening.

Comments

Honors College Award: Excellence in Research

Copyright

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Recommended Citation

Duong, Linh T., "Efficient Denoising and Sharpening of Color Images through Numerical Solution of Nonlinear Diffusion Equations" (2017). Honors Theses. 517.
https://aquila.usm.edu/honors_theses/517