Hanke-Raus heuristic rule for variational regularization in Banach spaces

Abstract

We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of Bregman distance. By imposing certain conditions on the random noise, we establish four convergence results; one relies on the source conditions and the other three do not depend on any source conditions. Numerical results are presented to illustrate the performance.

To appear in Inverse Problems

References in corpus (1)

• Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms

Cited by in corpus (4)

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• Convergence of Heuristic Parameter Choice Rules for Convex Tikhonov Regularisation
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• Dual gradient flow for solving linear ill-posed problems in Banach spaces