Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Authors:
G. Steidl;T. Teuber
Affiliations:
Dept. of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Dept. of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany
Venue:
Journal of Mathematical Imaging and Vision
Year:
2010

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Abstract

In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer for removing multiplicative Gamma noise. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizers of our restoration functionals by applying Douglas-Rachford splitting techniques, resp. alternating direction methods of multipliers. For a particular splitting, we present a semi-implicit scheme to solve the involved nonlinear systems of equations and prove its Q-linear convergence. Finally, we demonstrate the performance of our methods by numerical examples.