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.

翻译：本文讨论基于频率领域相关测量的大气声成像方法。 本领域的标准方法假定估计的关联矩阵与添加的白色噪音相加。 在本文中, 我们为测量过程提出了一个数学模型, 包括任意关联噪音。 相关数据的共变矩阵以第四顺序时间为单位提供。 本文的目的是探索在图像方法中如何使用测量数据的额外信息。 为此, 引入了一组加权数据空间, 每个数据空间自然地定义了具有相应点扩展功能的相关波形成像方法。 这个通用的相形体类别包含许多众所周知的方法, 如常规波形、 (RObust) 调制波形或以阴影成形。 本条特别研究了取决于噪音( co) 差异的加权。 在理论分析中, 我们证明, 由全噪变异矩阵加权的光谱, 与所述类别的所有光谱之间差异最小。 对合成和实验数据应用( CO) 加权法方法, 显示合成和实验数据的分辨率的改善是噪音的改善效果。