Discretization-adaptive regularization of inverse problems

We consider linear inverse problems under white (non-Gaussian) noise. For the solution we have to discretize the problem, and we consider a sequence of discretization schemes with increasing complexity. Starting from the coarsest discretization, we sequentially solve the discretized problems with standard methods (e.g., spectral cut-off and Landweber method together with the (heuristic) discrepancy principle). We additionally take into account the dynamics of the regularization parameters to decide when to stop the procedure adaptively. We discuss the accuracy and the computational costs of the final approximation.