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Explicit Nonflat Time Evolution for PDE-Based Image Restoration

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Computer Vision, Graphics and Image Processing

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4338))

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Abstract

This article is concerned with new strategies with which explicit time-stepping procedures of PDE-based restoration models converge with a similar efficiency to implicit algorithms. Conventional explicit algorithms often require hundreds of iterations to converge. In order to overcome the difficulty and to further improve image quality, the article introduces new spatially variable constraint term and timestep size, as a method of nonflat time evolution (MONTE). It has been verified that the explicit time-stepping scheme incorporating MONTE converges in only 4-15 iterations for all restoration examples we have tested. It has proved more effective than the additive operator splitting (AOS) method in both computation time and image quality (measured in PSNR), for most cases. Since the explicit MONTE procedure is efficient in computer memory, requiring only twice the image size, it can be applied particularly for huge data sets with a great efficiency in computer memory as well.

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Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, Mississippi State University, Mississippi State, MS, 39762, USA

    Seongjai Kim

  2. IMA, University of Minnesota, 207 Church Street S.E., Minneapolis, MN, 55455, USA

    Song-Hwa Kwon

Authors
  1. Seongjai Kim
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  2. Song-Hwa Kwon
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, IIT Delhi, New Delhi, India

    Prem K. Kalra

  2. School of Computer Science and Engineering, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Shmuel Peleg

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© 2006 Springer-Verlag Berlin Heidelberg

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Kim, S., Kwon, SH. (2006). Explicit Nonflat Time Evolution for PDE-Based Image Restoration. In: Kalra, P.K., Peleg, S. (eds) Computer Vision, Graphics and Image Processing. Lecture Notes in Computer Science, vol 4338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11949619_4

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  • DOI: https://doi.org/10.1007/11949619_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68301-8

  • Online ISBN: 978-3-540-68302-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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