A novel approach in polarimetric covariance matrix eigendecomposition

A new concept, the power normalized coherency matrix, is introduced to clarify the eigenvalue problem definition in SAR polarimetry. It is shown that the elements of the power normalized coherency matrix are good descriptors of polarimetric properties of SAR targets. An alternative scheme to alpha-entropy classification is proposed. It is shown that target entropy is closely related to the normalised coherency matrix determinant and the average alpha angle is related to the first element of the coherency matrix. This suggests that complicated eigenvalue calculations are not necessary in some SAR classification problems. The results also show that the average alpha and entropy parameters do not describe eigenvalue decomposition well, as similar parameters can be calculated without eigendecomposition. All results derived in this paper are based on general properties of Hermitian matrices.