Perturbation Analysis of Eigenvector-Based Target Decomposition Theorems in Radar Polarimetry

A novel analysis of the statistics of the eigendecomposition of the coherency matrix and the H/A/α̅ parameters of polarimetric synthetic aperture radar data is addressed. The objective is to overcome previous approaches that prevented the extraction of information about the sample eigenvectors or restricted the analysis to simulated data. This paper considers a perturbation analysis of the eigendecomposition of the coherency matrix, making it possible to obtain analytical expressions for the sample eigenvalues and their means and variances, the sample mean entropy and anisotropy, the sample eigenvectors and the sample αi angles, as well as for the sample mean alpha angle α̅. All the parameters are shown to be estimated asymptotically non-biased with respect to the number of averaged samples. It is also demonstrated that the sample eigenvectors are more robust than the sample eigenvalues to the presence of speckle. Finally, a simple technique for the precise removal of the entropy bias is presented.