In this work we introduce a formulation for a nonlocal Hessian that combines the ideas of higherorder and nonlocal regularization for image restoration, extending the idea of nonlocal gradients to higher-order derivatives. By intelligently choosing the weights, the model allows us to improve on the current state of the art higher-order method, total generalized variation, with respect to overall quality and preservation of jumps in the data. In the spirit of recent work by Brezis et al., our formulation also has analytic implications: for a suitable choice of weights it can be shown to converge to classical second-order regularizers, and in fact it allows a novel characterization of higher-order Sobolev and BV spaces.
Bibliographical noteKAUST Repository Item: Exported on 2021-10-08
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This project was supported by King Abdullah University of Science and Technology (KAUST) award KUK-I1-007-43.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Applied Mathematics