Geodesic
Iterative methods for solving the dual formulation arising from image restoration
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 299-311
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 
@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/}
}
TY  - JOUR
AU  - Chan,  Tony F.
AU  - Chen,  Ke
AU  - Carter,  Jamylle L.
TI  - Iterative methods for solving the dual formulation arising from image restoration
JO  - Electronic transactions on numerical analysis
PY  - 2007
SP  - 299
EP  - 311
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a9/
LA  - en
ID  - ETNA_2007__26__a9
ER  - 
%0 Journal Article
%A Chan,  Tony F.
%A Chen,  Ke
%A Carter,  Jamylle L.
%T Iterative methods for solving the dual formulation arising from image restoration
%J Electronic transactions on numerical analysis
%D 2007
%P 299-311
%V 26
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a9/
%G en
%F ETNA_2007__26__a9
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/