Author

Aaron Katchen

Document 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

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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