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Multiscale total variation regularization in image restoration

A 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. A local variance estimator is used to automatically adjust the regularization parameter. A generalized hierarchical decomposition of the restored image is integrated to the algorithm in order to speed‐up the performance of the update scheme. The corresponding subproblems are solved by a superlinearly convergent algorithm based on Fenchel‐duality and inexact semismooth Newton techniques. Numerical tests illustrate the performance of the algorithm. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)