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Texture Enhancing Based on Variational Image Decomposition

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Mathematical Image Processing

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 5))

Abstract

In this paper we consider the Augmented Lagrangian Method for image decomposition. We propose a method which decomposes an image into texture, which is characterized to have finite l 1 curvelet coefficients, a cartoon part, which has finite total variation norm, and noise and oscillating patterns, which have finite G-norm. In the second part of the paper we utilize the equivalence of the Augmented Lagrangian Method and the iterative Bregman distance regularization to show that the dual variables can be used for enhancing of particular components. We concentrate on the enhancing feature for the texture and propose two different variants of the Augmented Lagrangian Method for decomposition and12.5pc]The first author has been considered as corresponding author. Please check. enhancing.

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Author information

Authors and Affiliations

  1. Hauptstrasse 1c/1, 6074, Rinn, Austria

    Florian Frühauf

  2. Computational Science Center, University of Vienna, Nordbergstr. 15, 1090, Vienna, Austria

    Carsten Pontow & Otmar Scherzer

  3. Radon Institute of Computational and Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040, Linz, Austria

    Otmar Scherzer

Authors
  1. Florian Frühauf
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  2. Carsten Pontow
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  3. Otmar Scherzer
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Corresponding author

Correspondence to Otmar Scherzer .

Editor information

Editors and Affiliations

  1. , UMR 6628-MAPMO, Université d'Orléans, Orléans Cedex 2, 45067, France

    Maïtine Bergounioux

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Frühauf, F., Pontow, C., Scherzer, O. (2011). Texture Enhancing Based on Variational Image Decomposition. In: Bergounioux, M. (eds) Mathematical Image Processing. Springer Proceedings in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19604-1_7

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