Uniform Polarimetric Matrix Rotation Theory and Its Applications

This paper presents the development of a uniform polarimetric matrix rotation theory in the rotation domain along the radar line of sight for polarimetric synthetic aperture radar (PolSAR) data interpretation. The uniform representation of each coherency matrix element is a sinusoidal function in the rotation domain. A set of oscillation parameters, including oscillation amplitude, oscillation center, angular frequency, and initial angle, is proposed to fully characterize the scattering behavior in the rotation domain. A set of rotation angle parameters, including stationary angle, null angle, and minimization/maximization angles, is derived to indicate specific states of the rotation property. The rotation relationships between the coherency and covariance matrices with linear and circular polarization bases are established. A look-up table for these parameters is provided, and their physical meanings are interpreted. These derived parameters directly link to the Huynen parameters. Therefore, the proposed theory has the ability to achieve a desired state of one Huynen parameter by rotating the polarimetric matrix at a designated rotation angle. This theory also generalizes both the classic polarization orientation angle originally derived from the covariance matrix in a circular polarization basis and the deorientation theory developed from the minimization of the cross-polarization term. The roll-invariant terms have also been summarized. Finally, multifrequency Pi-SAR and AIRSAR PolSAR data sets are used to demonstrate the derived parameters. One oscillation amplitude parameter has been verified to be especially suitable for characterization of oriented man-made targets. Two angle parameters are sensitive to the reflection symmetry condition and crop types. Therefore, a simple unsupervised classification scheme has been developed and demonstrated. Further utilization perspectives of the proposed theory have been discussed.