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Volume 12, Issue 1
A Total Variation Discontinuous Galerkin Approach for Image Restoration

Benjamin Stamm & Thomas P. Wihler

Int. J. Numer. Anal. Mod., 12 (2015), pp. 81-93.

Published online: 2015-12

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  • Abstract

The focal point of this paper is to propose and analyze a $\mathbb{P}_0$ discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

  • Keywords

Discontinuous Galerkin methods, total variation image denoising, energy minimization methods, nonlinear elliptic filters.

  • AMS Subject Headings

65D18, 65N30, 68U10, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-81, author = {Benjamin Stamm and Thomas P. Wihler}, title = {A Total Variation Discontinuous Galerkin Approach for Image Restoration}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {1}, pages = {81--93}, abstract = {

The focal point of this paper is to propose and analyze a $\mathbb{P}_0$ discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/479.html} }
TY - JOUR T1 - A Total Variation Discontinuous Galerkin Approach for Image Restoration AU - Benjamin Stamm & Thomas P. Wihler JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 81 EP - 93 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/479.html KW - Discontinuous Galerkin methods, total variation image denoising, energy minimization methods, nonlinear elliptic filters. AB -

The focal point of this paper is to propose and analyze a $\mathbb{P}_0$ discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

Benjamin Stamm and Thomas P. Wihler. (2015). A Total Variation Discontinuous Galerkin Approach for Image Restoration. International Journal of Numerical Analysis and Modeling. 12 (1). 81-93. doi:
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