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We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear.
Convex analysis
Ralph Tyrell Rockafellar · 1972
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A mixed finite element method for 2-nd order elliptic problems
Pierre-Arnaud Raviart and Jean-Marie Thomas · 1977
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Duality for the sum of convex functions in general Banach spaces
Hédy Attouch and Haïm Brezis · 1986
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Nonlinear total variation based noise removal algorithms
Leonid I Rudin, Stanley Osher, and Emad Fatemi · 1992
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Segmentation of visual motion by minimizing convex non-quadratic functionals
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Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids
James M Hyman and Mikhail Shashkov · 1997
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Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
James M Hyman and Mikhail Shashkov · 1997
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Partial Differential Equations
Lawrence Craig Evans · 1998
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Denoising with higher order derivatives of bounded variation and an application to parameter estimation
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Convex analysis and variational problems
Ivar Ekeland and Roger Temam · 1999
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Functions of Bounded Variation and Free Discontinuity Problems
L. Ambrosio, N. Fusco, and D. Pallara · 2000
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Gamma-convergence for Beginners
Andrea Braides · 2002
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An iterative regularization method for total variation-based image restoration
Stanley Osher, Martin Burger, Donald Goldfarb, Jinjun Xu, and Wotao Yin · 2005
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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations
G. Aubert and P. Kornprobst · 2006
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Simultaneous higher-order optical flow estimation and decomposition
Jing Yuan, Christoph Schörr, and Gabriele Steidl · 2007
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Edge-based image compression with homogeneous diffusion
Markus Mainberger and Joachim Weickert · 2009
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Kristian Bredies, Karl Kunisch, and Thomas Pock · 2010
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A fourth order dual method for staircase reduction in texture extraction and image restoration problems
Higher-order TV methods – enhancement via Bregman iteration
Martin Benning, Christoph Brune, Martin Burger, and Jahn Müller · 2013
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Ground states and singular vectors of convex variational regularization methods
Martin Benning and Martin Burger · 2013
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Symmetric tensor fields of bounded deformation
Kristian Bredies · 2013
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A guide to the TV zoo
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Adaptive primal-dual hybrid gradient methods for saddle-point problems
Tom Goldstein, Min Li, Xiaoming Yuan, Ernie Esser, and Richard Baraniuk · 2013
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Regularization of linear inverse problems with total generalized variation
Kristian Bredies and Martin Holler · 2014
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