Numerical Methods for Source Power Reconstruction in Experimental Aeroacoustics

Abstract

We consider the inverse source problem of reconstructing the power of a bounded, compactly supported and uncorrelated acoustic source, given the covariance operator of pressure data within a bounded measurement domain. Such problems arise for example from aeroacoustic wind tunnel experiments. It turns out that in this case, the source power function is uniquely determined by the covariance operator. Given noisy correlation measurements, pointwise imaging methods provide a rough estimator of the source power. The resolution of such imaging methods can be increased by considering a weighted inner product in the data space, depending on the statistical properties of the measurement noise. For the reconstruction of the entire source power function, Tikhonov regularization with a sparsity promoting penalty functional is considered.