Locally adaptive image denoising by a statistical multiresolution criterion

Authors:
Thomas Hotz;Philipp Marnitz;Rahel Stichtenoth;Laurie Davies;Zakhar Kabluchko;Axel Munk
Affiliations:
Institute for Mathematical Stochastics, University of Göttingen, Goldschmidtstrasse 7, 37077 Göttingen, Germany;Institute for Mathematical Stochastics, University of Göttingen, Goldschmidtstrasse 7, 37077 Göttingen, Germany;Faculty of Mathematics, University of Duisburg-Essen, 45117 Essen, Germany;Faculty of Mathematics, University of Duisburg-Essen, 45117 Essen, Germany;Institute for Mathematical Stochastics, University of Göttingen, Goldschmidtstrasse 7, 37077 Göttingen, Germany;Institute for Mathematical Stochastics, University of Göttingen, Goldschmidtstrasse 7, 37077 Göttingen, Germany
Venue:
Computational Statistics & Data Analysis
Year:
2012

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Abstract

It is shown how to choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, an efficient method for locally adaptive image denoising is presented. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples together with applications in confocal microscopy illustrate the usefulness of the approach.