TY - GEN A1 - Wachsmuth, Gerd A1 - Herrmann, Marc A1 - Herzog, Roland A1 - Schmidt, Stephan A1 - Vidal-Núñez, José T1 - Discrete Total Variation with Finite Elements and Applications to Imaging T2 - Journal of Mathematical Imaging and Vision : (JMIV) N2 - 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-L2 and TV-L1, 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. KW - Discrete total variaton KW - Dual problem KW - Image reconstruction KW - Numerical algorithms Y1 - 2019 U6 - https://doi.org/10.1007/s10851-018-0852-7 SN - 0924-9907 SN - 1573-7683 VL - 61 IS - 4 SP - 411 EP - 431 ER -