期刊
JOURNAL OF MATHEMATICAL IMAGING AND VISION
卷 61, 期 4, 页码 411-431出版社
SPRINGER
DOI: 10.1007/s10851-018-0852-7
关键词
Discrete total variation; Dual problem; Image reconstruction; Numerical algorithms
类别
资金
- DFG [HE 6077/10-1, SCHM 3248/2-1, SPP 1962]
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is defined. DTV has favorable properties, compared to the original TV-seminorm for finite element functions. These include a convenient dual representation in terms of the supremum over the space of Raviart-Thomas finite element functions, subject to a set of simple constraints. It can therefore be shown that a variety of algorithms for classical image reconstruction problems, including TV-L-2 denoising and inpainting, can be implemented in low- and higher-order finite element spaces with the same efficiency as their counterparts originally developed for images on Cartesian grids.
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