A Class of Fast Algorithms for Total Variation Image Restoration

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Author:

Junfeng Yang, Wotao Yin, Yilun Wang, Yin Zhang

Subject:

Mathematics and Statistics, Science and Technology

Institution Name:

Connexions

Collection:

Connexions

Grade Level:

Post-secondary

Abstract:

This report summarizes work done as part of the Imaging and Optimization PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem. This module is based on the recent work of Junfeng Yang (jfyang2992@yahoo.com.cn) from Nanjing University and Wotao Yin, Yin Zhang, and Yilun Wang (wotao.yin, yzhang, yilun.wang@rice.edu) from Rice University. In image formation, the observed images are usually blurred by optical instruments and/or transfer medium and contaminated by noise, which makes image restoration a classical problem in image processing. Among various variational deconvolution models, those based upon total variation (TV) are known to preserve edges and meanwhile remove unwanted fine details in an image and thus have attracted much research interests since the pioneer work by Rudin, Osher and Fatemi. However, TV based models are difficult to solve due to the nondifferentiability and the universal coupling of variables. In this module, we present, analyze and test a class of alternating minimization algorithms for reconstructing images from blurry and noisy observations with TV-like regularization. This class of algorithms are applicable to both single- and multi-channel images with either Gaussian or impulsive noise, and permit cross-channel blurs when the underlying image has more than one channels. Numerical results are given to demonstrate the effectiveness of the proposed algorithms.

Course Type:

Learning Module

Languages:

English

Material Type:

Readings

Media Format:

Text/HTML, Downloadable docs

Conditions of Use:

Creative Commons Attribution 2.0