Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part I: Modelling and Theory |
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Authors: | Michael Hintermüller Carlos N. Rautenberg |
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Affiliation: | 1.Weierstrass Institute,Berlin,Germany;2.Department of Mathematics,Humboldt-University of Berlin,Berlin,Germany |
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Abstract: | A weighted total variation model with a spatially varying regularization weight is considered. Existence of a solution is shown, and the associated Fenchel predual problem is derived. For automatically selecting the regularization function, a bilevel optimization framework is proposed. In this context, the lower-level problem, which is parameterized by the regularization weight, is the Fenchel predual of the weighted total variation model and the upper-level objective penalizes violations of a variance corridor. The latter object relies on a localization of the image residual as well as on lower and upper bounds inspired by the statistics of the extremes. |
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