A class of quasi-variational inequalities for adaptive image denoising and decomposition
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- Lenzen, F., Becker, F., Lellmann, J. et al. Comput Optim Appl (2013) 54: 371. doi:10.1007/s10589-012-9456-0
We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.