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An Iterative Regularization Algorithm for the TV-Stokes in Image Processing

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Parallel Processing and Applied Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9574))

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Abstract

Image denoising is one of the fundamental problems in the image processing. In a PDE based approach for image processing, the simplest possible method for denoising is to solve the heat equation. However such a diffusion equation will destroy sharp edges in the image. An approach known for preserving the edges while denoising is called the classical Rudin-Osher-Fatemi (ROF) method based on the total variation (TV) regularization. Recently, an algorithm, also known as the TV-Stokes, based on two minimization steps involving the smoothing of the tangential field and then the reconstruction of the image has been proposed. The latter produces images without the blocky effect which we observe in the case of the ROF model. An iterative regularization method for the total variation based image restoration has recently been proposed giving significant improvement over the classical method in the quality of the restored image. In this paper we propose a similar algorithm for the TV-Stokes denoising algorithm.

L. Marcinkowski—This work was partially supported by Polish Scientific Grant N/N201/0069/33.

T. Rahman—The author acknowledges the support of NRC through DAADppp project 233989.

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Acknowledgements

We would like to thank Bin Wu for the numerical experiments.

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Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Leszek Marcinkowski

  2. Department of Computing, Mathematics and Physics, Bergen University College, Inndalsveien 28, 5063, Bergen, Norway

    Talal Rahman

Authors
  1. Leszek Marcinkowski
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  2. Talal Rahman
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Corresponding author

Correspondence to Leszek Marcinkowski .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Marcinkowski, L., Rahman, T. (2016). An Iterative Regularization Algorithm for the TV-Stokes in Image Processing. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_36

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  • DOI: https://doi.org/10.1007/978-3-319-32152-3_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32151-6

  • Online ISBN: 978-3-319-32152-3

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