Applications of integrals of quadratic forms for polarimetric SAR data

Quadratic forms play an important role in Polarimetric and Interferometric Synthetic Aperture Radar (Pol-InSAR) images. This work is aimed at solving (rigorously and with approximations) the integrals of quadratic forms. Specifically, it is possible to derive that the integral of the quadratic form of covariance matrices (i.e. power of a polarization channel) is equal to the third part of the matrix Trace. Additionally, the integral of the Pol-InSAR coherence (expressed with quadratic forms) can be approximated with the same expression where the quadratic forms are substituted by Trace operators. The derived equations are tested on real ESAR (DLR) quad-polarimetric data.