The Lepskii Principle for an Inverse Source Problem in Experimental Aeroacoustics

Abstract

This conference contribution is concerned with variational inverse methods (e.g. generalized Tikhonov regularization) in experimental aeroacoustics that seek to reconstruct the source power function of an aeroacoustic source from measured correlation data. We investigate a Tikhonov functional composed of a quadratic data misfit functional and a sparsity promoting regularization functional. For an optimal accuracy of the reconstruction, the choice of the regularization parameter is crucial. The Lepski˘ı principle is a parameter choice strategy that is well understood from a mathematical point of view. We will present a procedure, how the Lepski˘ı principle can be applied to the aeroacoustic inverse source problem. The procedure relies on a Monte Carlo simulation of the propagated data noise error. The source sampling for the Monte Carlo simulation is motivated by the probabilistic setup presented in [HS17]. Furthermore it makes use of the data error statistics that were investigated in [RSHE20].