@Article{Hintermüller2017,
author="Hinterm{\"u}ller, Michael
and Rautenberg, Carlos N.",
title="Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part I: Modelling and Theory",
journal="Journal of Mathematical Imaging and Vision",
year="2017",
month="Nov",
day="01",
volume="59",
number="3",
pages="498--514",
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.",
issn="1573-7683",
doi="10.1007/s10851-017-0744-2",
url="https://doi.org/10.1007/s10851-017-0744-2"
}