Stochastic asymptotical regularization for linear inverse problems

Abstract We introduce stochastic asymptotical regularization (SAR) methods for the uncertainty quantification of stable approximate solution ill-posed linear-operator equations, which are deterministic models numerous inverse problems in science and engineering. demonstrate that SAR can quantify error estimates problems. prove regularizing properties with regard to mean-square convergence. also show is an order-optimal method linear provided terminating time chosen according smoothness solution. This result proven both a priori posteriori stopping rules under general range-type source conditions. Furthermore, some converse results verified. Two iterative schemes developed numerical realization SAR, convergence analyses these two provided. A toy example real-world problem biosensor tomography studied accuracy advantages SAR: compared conventional approaches problems, provide quantity interest, turn be used reveal explicate hidden information about usually obscured by incomplete mathematical modeling ascendence complex-structured noise.