Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise
Inverse Problems and Imaging2008Vol. 2(2), pp. 271–290
Citations Over TimeTop 10% of 2008 papers
Abstract
We consider the inverse problem to identify coefficient functions in boundary value problems from noisy measurements of the solutions. Our estimators are defined as minimizers of a Tikhonov functional, which is the sum of a nonlinear data misfit term and a quadratic penalty term involving a Hilbert scale norm. In this abstract framework we derive estimates of the expected squared error under certain assumptions on the forward operator. These assumptions are shown to be satisfied for two classes of inverse elliptic boundary value problems. The theoretical results are confirmed by Monte Carlo simulations.
Related Papers
- → GCV for Tikhonov regularization via global Golub–Kahan decomposition(2016)53 cited
- → A fast multiscale Galerkin method for ill-posed integral equations with notexactly given input data via Tikhonov regularization(2012)6 cited
- → Solving the Inverse Problem of Electrocardiography in a Realistic Environment Using a Spatio-Temporal LSQR-Tikhonov Hybrid Regularization Method(2009)2 cited
- NAH Theory and Simulation Based on Statistical Optimization(2014)
- On New Algorithm for TDOA Location Based on Tikhonov Regularization Theory(2009)