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A Range Condition for Polyconvex Variational Regularization by Kirisits, Clemens; Scherzer, Otmar is a scholarly article available to read on EtoBox.

What is A Range Condition for Polyconvex Variational Regularization about?

In the context of convex variational regularization it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequalities imply range conditions, while the converse implication only holds under an additional restriction on the operator. In this article we prove the analogous result for polyconvex regularization. More precisely, we show that the variational inequality derived by Kirisits, Scherzer (2017) implies that the derivative of the regularization functional must lie in the range of the dual-adjoint of the derivative of the operator. In addition, we show how to adapt the restriction on the operator in order to obtain the converse implication.

Author

Kirisits, Clemens; Scherzer, Otmar

Published

2018

Language

EN