Geodesic
Iterative methods for solving the dual formulation arising from image restoration
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 299-311.

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Summary: Many variational models for image denoising restoration are formulated in primal variables that are directly linked to the solution to be restored. If the total variation related semi-norm is used in the models, one consequence is that extra regularization is needed to remedy the highly non-smooth and oscillatory coefficients for effective numerical solution. The dual formulation was often used to study theoretical properties of a primal formulation. However as a model, this formulation also offers some advantages over the primal formulation in dealing with the above mentioned oscillation and non-smoothness. This paper presents some preliminary work on speeding up the Chambolle method [J. Math. Imaging Vision, 20 (2004), pp. 89-97] for solving the dual formulation.
Classification : 68U10, 65F10, 65K10
Keywords: image restoration, nonlinear partial differential equations, singularity, nonlinear iterations, Fourier analysis, multigrid method 
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     author = {Chan, Tony F. and Chen, Ke and Carter, Jamylle L.},
     title = {Iterative methods for solving the dual formulation arising from image restoration},
     journal = {Electronic transactions on numerical analysis},
     pages = {299--311},
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     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a9/}
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Chan, Tony F.; Chen, Ke; Carter, Jamylle L. Iterative methods for solving the dual formulation arising from image restoration. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 299-311. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a9/