Geodesic
Iterative methods for solving the dual formulation arising from image restoration
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 299-311
Zbl   EuDML
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 
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/
@article{ETNA_2007__26__a9,
     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},
     year = {2007},
     volume = {26},
     zbl = {1178.68620},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a9/}
}
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