The Eigenvector-Eigenvalue Identity Applied to Fast Calculation of polSAR Scattering Characterization

Unlike the original Cloude–van Zyl decomposition of reflection symmetric polarimetric synthetic aperture radar (polSAR) data, a recently suggested version of the decomposition for full/quad pol data relies on the Cloude–Pottier mean alpha angle (
${\bar {\alpha }}$
) to characterize the scattering mechanism.
${\bar {\alpha }}$
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
${\bar {\alpha }}$
by means of eigenvalues of the
$3\,\,{\times }$
3 coherency matrix and its
$2\,\,{\times }$
2 minor(s) only and is well suited for fast array-based computer implementation. In this letter with focus on computational aspects, we demonstrate fast EEI-based determination of
${\bar {\alpha }}$
on X-band Flugzeug synthetic aperture radar (F-SAR) image data over Vejers, Denmark, including a detailed example of calculations and computer code.