Necessary conditions for variational regularization schemes

Details Necessary conditions for variational regularization schemes Necessary conditions for variational regularization schemes

2012-04-03

arxiv.org/abs/1204.0649v1

Mathematics

Functional Analysis

Scientific paper

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: What are necessary conditions for a variational method to provide a regularization method? To this end, we formalize the notion of a variational scheme and compare three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions.

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