Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland.
Sensors (Basel). 2012;12(3):2766-86. doi: 10.3390/s120302766. Epub 2012 Mar 1.
Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.
多通道系统在科学的多个应用领域中都有出现。在合成孔径雷达 (SAR) 中，多通道系统可能指的是不同的领域，如多极化、多干涉或多时相数据，甚至是它们的组合。由于 SAR 图像中存在固有的斑点现象，因此几乎必须对数据进行统计描述才能加以利用。在一般情况下，在自然介质上获取的复图像具有零均值圆形高斯特性。在这种情况下，二阶统计量（如多通道协方差矩阵）可以完全描述数据。然而，对于实际情况，必须使用有限数量的样本估计协方差矩阵，而该样本协方差矩阵服从复 Wishart 分布。在这种情况下，多通道协方差矩阵的特征分解在与成像场景的物理特性相关的多个领域中都有重要应用。具体来说，协方差矩阵的最大特征值在不同的应用中经常被用作目标或变化检测、极化数据中主要散射机制的估计、动目标指示等。在本文中，简化了从样本多通道协方差矩阵的特征分解中推导出的最大特征值在多通道 SAR 图像中的统计行为，以方便 SAR 领域的使用。针对模拟数据进行了验证，并给出了使用解析表达式进行估计和检测问题的示例。
