A class of quasi-variational inequalities for adaptive image denoising and decomposition

作者：Lenzen Frank^*; Becker Florian; Lellmann Jan; Petra Stefania; Schnoerr Christoph

来源：Computational Optimization and Applications, 2013, 54(2): 371-398.

DOI：10.1007/s10589-012-9456-0

• Quasi-variational inequalities
• Adaptive image denoising
• Total variation regularization
• Solution-dependent adaptivity

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.

• 出版日期2013-3