Optimal selection of the regularization function in a generalized total variation model. Part I: Modelling and theory
- Hintermüller, Michael
- Rautenberg, Carlos N.
2010 Mathematics Subject Classification
- 94A08 68U10 49K20 49K30 49K40 49M37 65K15
- Image restoration, generalized total variation regularization, spatially distributed regularization weight, Fenchel predual, bilevel optimization, variance corridor
A generalized 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 generalized 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.
- J. Math. Imaging Vision, 59 (2017), pp. 498--514.