Volume scattering power restriction based on correlation coefficients for polarimetric SAR model-based decompositions

A validation method for polarimetric SAR model-based decompositions is proposed based on correlation coefficients between polarizations. The correlation coefficient is examined if it ranges from 0 to 1 for covariance matrices after the subtraction of volumetric scattering components. The three combinations of the polarizations seen in covariance matrices are examined. It is confirmed that, in general, the condition above is not held, which clarifies the overestimate of volume scattering, even though conventional procedures take negative powers into account. Furthermore, the possible maximal power of volume scattering is estimated by employing the condition as a constraint. The constraint by correlation coefficients is a part of the one by nonnegative eigenvalues. In order to equalize them, the third-order principal minor, that is the determinant in the case of 3*3 matrices, must be considered. Finally, the possible maximal power, equal to the one derived from the constraint by nonnegative eigenvalues, can be derived analytically, while that is estimated numerically for the case of nonnegative eigenvalues.