Compensation of Modeling Errors for the Aeroacoustic Inverse Problem with Tools from Deep Learning

Abstract

In the field of aeroacoustic source imaging, one seeks to reconstruct acoustic source powers from microphone array measurements. For most setups, one cannot expect a perfect reconstruction. The main effects that contribute to this reconstruction error are data noise and modeling errors. While the data noise is accounted for in most advanced reconstruction methods, e.g., by a proper regularization strategy, the modeling error is usually neglected. This article proposes an approach that extends regularized inverse methods with a mechanism that takes the modeling error into account. The presented algorithmic framework utilizes the representation of the Fast Iterative Shrinkage Thresholding Algorithm (FISTA) algorithm by a neural network and uses standard gradient schemes from the field of deep learning. It is directly applicable to a single measurement, i.e., a prior training phase on previously generated data is not required. The capabilities of the method are illustrated by several numerical examples.