Degree Type
Honors Capstone Project
Date of Submission
Spring 5-1-2011
Capstone Advisor
Professor Lixin Shen
Honors Reader
Professor Yuesheng Xu
Capstone Major
Mathematics
Capstone College
Arts and Science
Audio/Visual Component
no
Capstone Prize Winner
no
Won Capstone Funding
no
Honors Categories
Sciences and Engineering
Subject Categories
Applied Mathematics
Abstract
The following paper discusses how efficient and effective color image noise reduction may be achieved through the use of mathematic numerical analysis. Digital image noise is a longstanding problem for which efficient and effective solutions are critical to the advancement of the field of digital imaging. Micchelli-Shen-Xu [3] used the Total Variation Model in conjunction with proximity operators to propose a set of algorithms to effectively and efficiently solve for noisy grayscale images. They proposed the use of the proximity operator in anisotropic and isotropic total variation in fixed point algorithms. The following paper will discuss their algorithms as well as expand and implement these algorithms to apply to color images as well. When reducing noise in color images we may either apply the fixed point algorithm proposed by Micchelli-Shen-Xu [3] to the luma channel of YCbCr colorspace or apply the algorithm in parallel to the R G B channels of RGB colorspace. The later algorithm will produce better results at the expense of efficiency. 2
Recommended Citation
Katchen, Aaron, "Color Image Noise Reduction with the Total Variation Model and Proximity Operators" (2011). Honors Capstone Projects - All. 246.
https://surface.syr.edu/honors_capstone/246
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
