Chan, Tony F.; Chen, Ke; Carter, Jamylle L.

Iterative methods for solving the dual formulation arising from image restoration

ETNA, Electron. Trans. Numer. Anal. 26, 299-311, electronic only (2007)


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.

Mathematics Subject Classification

68U10, 65F10, 65K10


image restoration, nonlinear partial differential equations, singularity, nonlinear iterations, Fourier analysis, multigrid method