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Approximate Methods for Constrained Total Variation Minimization

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Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

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Abstract

Constrained total variation minimization and related convex optimization problems have applications in many areas of image processing and computer vision such as image reconstruction, enhancement, noise removal, and segmentation. We propose a new method to approximately solve this problem. Numerical experiments show that this method gets close to the globally optimal solution, and is 15-100 times faster for typical images than a state-of-the-art interior point method. Our method’s denoising performance is comparable to that of a state-of-the-art noise removal method of [4]. Our work extends our previously published algorithm for solving the constrained total variation minimization problem for 1D signals [13] which was shown to produce the globally optimal solution exactly in O(Nlog N) time where N is the number of data points.

This work was supported in part by the National Science Foundation (NSF) through CAREER award CCR-0093105 and through grant IIS-0329156.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Ave., West Lafayette, IN, 47907, USA

    Xiaogang Dong & Ilya Pollak

Authors
  1. Xiaogang Dong
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  2. Ilya Pollak
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Editor information

Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Dong, X., Pollak, I. (2006). Approximate Methods for Constrained Total Variation Minimization. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_41

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  • DOI: https://doi.org/10.1007/11753728_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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