Analysis and application of a nonlocal Hessian

Jan Lellmann, Konstantinos Papafitsoros, Carola Schönlieb, Daniel Spector

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)2161-2202
頁數42
期刊SIAM Journal on Imaging Sciences
8
發行號4
DOIs
出版狀態已發佈 - 2015 10月 6
對外發佈

ASJC Scopus subject areas

  • 數學(全部)
  • 應用數學

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