標題: Analysis and Application of a Nonlocal Hessian
作者: Lellmann, Jan
Papafitsoros, Konstantinos
Schoenlieb, Carola
Spector, Daniel
應用數學系
Department of Applied Mathematics
關鍵字: nonlocal Hessian;nonlocal total variation regularization;variational methods;fast marching method;amoeba filters
公開日期: 1-一月-2015
摘要: 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.
URI: http://dx.doi.org/10.1137/140993818
http://hdl.handle.net/11536/129603
ISSN: 1936-4954
DOI: 10.1137/140993818
期刊: SIAM JOURNAL ON IMAGING SCIENCES
起始頁: 2161
結束頁: 2202
顯示於類別:期刊論文