We examine relations between popular variational methods in image processing and classical operator splitting methods in convex analysis. We focus on a gradient descent reprojection algorithm for image denoising and the recently proposed Split Bregman and alternating Split Bregman methods. By identifying the latter with the so-called Douglas-Rachford splitting algorithm we can guarantee its convergence. We show that for a special setting 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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Setzer, S. (2009). Split bregman algorithm, douglas-rachford splitting and frame shrinkage. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5567 LNCS, pp. 464–476). https://doi.org/10.1007/978-3-642-02256-2_39
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