Search

We consider the variational regularization for inverse problems in a general form. Based on the discrepancy principle, we propose a heuristic parameter choice rule for choosing the regularization parameter which does not require the information on the noise level and is therefore purely data driven. Under variational source conditions, we obtain a posteriori error estimates. According to the Bakushinskii veto, convergence in the worst case scenario cannot be expected in general. However, by imposing certain conditions on the noisy data, we establish a convergence result for the heuristic rule. Applications of the results are addressed and numerical simulations are reported. [ABSTRACT FROM AUTHOR]

In this paper, an inverse Robin problem for an elliptic equation is investigated. The Robin coefficient is assumed to be a small perturbation from a reference coefficient, hence a sparse structure is a priori known. An Lq-regularized output least square formulation is considered with q ∈ (0,1). The existence of the minimizer is proved. The convergence of the finite element discretization with respect to mesh size is shown. A modified Newton algorithm is applied to solve the smoothing first order optimality system. Two-dimensional and three-dimensional numerical examples demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]