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Module by: Junfeng Yang, Wotao Yin, Yin Zhang, Yilun Wang. E-mail the authors

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Name: A Class of Fast Algorithms for Total Variation Image Restoration
ID: m19059
Language: English (en)
Summary: 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.
Subject: Mathematics and Statistics, Science and Technology
Keywords: color image, image deblurring, image deconvolution, image denoising, optimization, total variation
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 2.0

Authors: Junfeng Yang (jfyang2992@yahoo.com.cn), Wotao Yin (wotao.yin@rice.edu), Yin Zhang (yzhang@rice.edu), Yilun Wang (yilun.wang@gmail.com)
Copyright Holders: Junfeng Yang (jfyang2992@yahoo.com.cn), Wotao Yin (wotao.yin@rice.edu), Yin Zhang (yzhang@rice.edu), Yilun Wang (yilun.wang@gmail.com)
Maintainers: Junfeng Yang (jfyang2992@yahoo.com.cn), Wotao Yin (wotao.yin@rice.edu), Yin Zhang (yzhang@rice.edu), Yilun Wang (yilun.wang@gmail.com)

Latest version: 1.2 (history)
First publication date: Dec 24, 2008 9:22 pm +0000
Last revision to module: Dec 26, 2008 10:21 am +0000

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Version History

Version: 1.2 Dec 26, 2008 10:21 am +0000 by Wotao Yin
Changes:
Updated summary and acknowledgements to include VIGRE info

Version: 1.1 Dec 26, 2008 10:11 am +0000 by Wotao Yin
Changes:
Initial publication

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American Chemical Society (ACS) Style Guide:

Yang, J.; Yin, W.; Zhang, Y.; Wang, Y. A Class of Fast Algorithms for Total Variation Image Restoration, OpenStax-CNX Web site. http://cnx.org/content/m19059/1.2/, Dec 26, 2008.

American Medical Assocation (AMA) Manual of Style:

Yang J, Yin W, Zhang Y, Wang Y. A Class of Fast Algorithms for Total Variation Image Restoration [OpenStax-CNX Web site]. December 26, 2008. Available at: http://cnx.org/content/m19059/1.2/.

American Psychological Assocation (APA) Publication Manual:

Yang, J., Yin, W., Zhang, Y., & Wang, Y. (2008, December 26). A Class of Fast Algorithms for Total Variation Image Restoration. Retrieved from the OpenStax-CNX Web site: http://cnx.org/content/m19059/1.2/

Chicago Manual of Style (Bibliography):

Yang, Junfeng, Wotao Yin, Yin Zhang, and Yilun Wang. "A Class of Fast Algorithms for Total Variation Image Restoration." OpenStax-CNX. December 26, 2008. http://cnx.org/content/m19059/1.2/.

Chicago Manual of Style (Note):

Junfeng Yang and others, "A Class of Fast Algorithms for Total Variation Image Restoration," OpenStax-CNX, December 26, 2008, http://cnx.org/content/m19059/1.2/.

Chicago Manual of Style (Reference, in Author-Date style):

Yang, J., Yin, W., Zhang, Y., & Wang, Y. 2008. A Class of Fast Algorithms for Total Variation Image Restoration. OpenStax-CNX, December 26, 2008. http://cnx.org/content/m19059/1.2/.

Modern Languages Association (MLA) Style Manual:

Yang, Junfeng, Wotao Yin, Yin Zhang, and Yilun Wang. A Class of Fast Algorithms for Total Variation Image Restoration. OpenStax-CNX. 26 Dec. 2008 <http://cnx.org/content/m19059/1.2/>.