A multi-scale total variation model for image restoration is introduced. The model utilizes a spatially dependent regularization parameter in order to enhance image regions containing details while still sufficiently smoothing homogeneous features. The fully automated adjustment strategy of the regularization parameter is based on local variance estimators. For robustness reasons, the decision on the acceptance or rejection of a local parameter value relies on a confidence interval technique based on the expected maximal local variance estimate. In order to speed-up the performance of the update scheme a generalized hierarchical decomposition of the restored image is used. The corresponding subproblems are solved by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques. The paper ends by a report on numerical tests, a qualitative study of the proposed adjustment scheme and a comparison with popular total variation based restoration methods.

A total variation (TV) model with a L 1 -fidelity term and a spatially adapted regularization parameter is presented in order to reconstruct images contaminated by impulse noise. This model intends to preserve small details while homogeneous features still remain smooth. The regularization parameter is locally adapted according to a local expected absolute value estimator depending on the statistical characteristics of the noise. The numerical solution of the L 1 -TV minimization problem with a spatially adapted parameter is obtained by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques, which is stable with respect to noise in the data. Numerical results justifying the advantage of such a regularization parameter choice rule are presented.

A general multi-scale vectorial total variation model with spatially adapted regularization parameter for color image restoration is introduced in this paper. This total variation model contains an L τ -data fidelity for any τ ∈ [1, 2]. The use of a spatial dependent regularization parameter improves the reconstruction of features in the image as well as an adequate smoothing for the homogeneous parts. The automated adaptation of this regularization parameter is made according to local statistical characteristics of the noise which contaminates the image. The corresponding multiscale vectorial total variation model is solved by Fenchel-duality and inexact semismooth Newton techniques. Numerical results are presented for the cases τ = 1 and τ = 2 which reconstruct images contaminated with saltand-pepper noise and Gaussian noise, respectively.

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