Abstract
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.
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Keywords
- Maximal Monotone Operator
- Proximal Point Algorithm
- Augmented Lagrangian Method
- Wavelet Shrinkage
- Parseval Frame
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Setzer, S. (2009). Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_39
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DOI: https://doi.org/10.1007/978-3-642-02256-2_39
Publisher Name: Springer, Berlin, Heidelberg
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