Analysis and Application of a Nonlocal Hessian
Authors: 
Jan Lellmann, Konstantinos Papafitsoros, Carola Schönlieb, Daniel SpectorAuthors Info & Claims
Pages 2161 - 2202
Abstract
In this work we introduce a formulation for a nonlocal Hessian that combines the ideas of higher-order 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.
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Published: 01 January 2015
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