Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors
Abstract
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such functions. These regularization functionals are motivated from double integrals, which approximate Sobolev semi-norms of intensity functions. These were introduced in Bourgain, Br\'ezis and Mironescu, "Another Look at Sobolev Spaces". In: Optimal Control and Partial Differential Equations-Innovations and Applications, IOS press, Amsterdam, 2001. For the proposed regularization functionals we prove existence of minimizers as well as a stability and convergence result for functions with values in a set of vectors.
Keywords
Cite
@article{arxiv.1805.07552,
title = {Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors},
author = {René Ciak and Melanie Melching and Otmar Scherzer},
journal= {arXiv preprint arXiv:1805.07552},
year = {2018}
}