  This article discusses aeroacoustic imaging methods based on correlation
measurements in the frequency domain. Standard methods in this field assume
that the estimated correlation matrix is superimposed with additive white
noise. In this paper we present a mathematical model for the measurement
process covering arbitrarily correlated noise. The covariance matrix of
correlation data is given in terms of fourth order moments. The aim of this
paper is to explore the use of such additional information on the measurement
data in imaging methods. For this purpose a class of weighted data spaces is
introduced, where each data space naturally defines an associated beamforming
method with a corresponding point spread function. This generic class of
beamformers contains many well-known methods such as Conventional Beamforming,
(Robust) Adaptive Beamforming or beamforming with shading. This article
examines in particular weightings that depend on the noise (co)variances. In a
theoretical analysis we prove that the beamformer, weighted by the full noise
covariance matrix, has minimal variance among all beamformers from the
described class. Application of the (co)variance weighted methods on synthetic
and experimental data show that the resolution of the results is improved and
noise effects are reduced.
