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IJCV
2011

Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing

12 years 6 months ago
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
We examine the underlying structure of popular algorithms for variational methods used in image processing. We focus here on operator splittings and Bregman methods based on a unified approach via fixed point iterations and averaged operators. In particular, the recently proposed alternating split Bregman method can be interpreted from different points of view - as a Bregman, as an augmented Lagrangian and as a Douglas-Rachford splitting algorithm which is a classical operator splitting method. We also study similarities between this method and the forward-backward splitting method when applied to two frequently used models for image denoising which employ a Besov-norm and a total variation regularization term, respectively. In the first setting, we show that for a discretization based on Parseval frames the gradient descent reprojection and the alternating split Bregman algorithm are equivalent and turn out to be a frame shrinkage method. For the total variation regularizer, we als...
Simon Setzer
Added 29 Aug 2011
Updated 29 Aug 2011
Type Journal
Year 2011
Where IJCV
Authors Simon Setzer
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