The eigenvector-eigenvalue identity applied to fast calculation of polSAR scattering characterization

Unlike the original Cloude-van Zyl decomposition of reflection symmetric polSAR data, a recently suggested version of the decomposition for full/quad pol data relies on the Cloude-Pottier mean alpha angle (ᾱ) to characterize the scattering mechanism. ᾱ can be calculated from the eigenvectors of the coherency matrix. By means of the eigenvector-eigenvalue identity (EEI) we can avoid the calculation of the eigenvectors. The EEI finds ᾱ by means of eigenvalues of the 3×3 coherency matrix and its 2×2 minor(s) only and is well suited for fast array based computer implementation. In this paper with focus on computational aspects we demonstrate fast EEI based determination of ᾱ on X-band F-SAR image data over Vejers, Denmark, including a detailed example of calculations and computer code.