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Unlike the original Cloude&#x2013;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&#x2013;Pottier mean alpha angle (<inline-formula> <tex-math notation="LaTeX">${\bar {\alpha }}$ </tex-math></inline-formula>) to characterize the scattering mechanism. <inline-formula> <tex-math notation="LaTeX">${\bar {\alpha }}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">${\bar {\alpha }}$ </tex-math></inline-formula> by means of eigenvalues of the <inline-formula> <tex-math notation="LaTeX">$3\,\,{\times }$ </tex-math></inline-formula> 3 coherency matrix and its <inline-formula> <tex-math notation="LaTeX">$2\,\,{\times }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">${\bar {\alpha }}$ </tex-math></inline-formula> on X-band Flugzeug synthetic aperture radar (F-SAR) image data over Vejers, Denmark, including a detailed example of calculations and computer code.

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