We kindly invite you to the talk "Regularising linear inverse problems under unknown non-Gaussian noise" by Tim Jahn. Wednesday, Jan. 27th, 13:00 Vienna Time.

Online at: https://meet.csc.univie.ac.at/b/axe-7hr-2ad

We deal with the solution of linear ill-posed equations in Hilbert spaces. Usually, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications such ad hoc knowledge may often be unrealistic. However, the error of a measurement may often be estimated through averaging of repeated measurements. We combine this with classical Filter-based regularisation methods for a purely data-driven regularisation scheme. We obtain convergence to the true solution, with the only assumption that the measurements are unbiased, independent and identically distributed according to an elseways arbitrary unknown distribution (with finite variance or of white noise type). Moreover, we analyse the discrepancy principle as an adaptive stopping rule for a stochastic gradient descent, as a non-Filter based computationally efficient regularisation method.