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Unformatted text preview: Connexions module: m19059 1 A Class of Fast Algorithms for Total Variation Image Restoration * Junfeng Yang Wotao Yin Yin Zhang Yilun Wang This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † 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 ([email protected]) from Nanjing University and Wotao Yin, Yin Zhang, and Yilun Wang (wotao.yin, yzhang, [email protected]) 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 process- ing. Among various variational deconvolution models, those based upon total variation (TV) are known to preserve edges and meanwhile remove unwanted ne 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 di cult to solve due to the nondi erentiability 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 e ectiveness of the proposed algorithms. 1 Introduction In electrical engineering and computer science, image processing refers to any form of signal processing in which the input is an image and the output can be either an image or a set of parameters related to the image. Generally, image processing includes image enhancement, restoration and reconstruction, edge and boundary detection, classi cation and segmentation, object recognition and identi cation, compression and communication, etc. Among them, image restoration is a classical problem and is generally a preprocessing * Version 1.2: Dec 26, 2008 10:21 am US/Central † http://creativecommons.org/licenses/by/2.0/ http://cnx.org/content/m19059/1.2/ Connexions module: m19059 2 stage of higher level processing. In many applications, the measured images are degraded by blurs; e.g....
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