Polarimetric contrast enhancement coefficients for perfecting high-resolution POL-SAR/SAL image feature extraction

In microwave remote sensing, it is desirable to select radar antenna polarizations that maximize the contrast between two classes of scatterers or scatterer ensembles. A polarimetric radar measures complete polarization properties of a target and then provides a vector description of the resulting scattered wave through various target matrices. Several optimization procedures for the completely and partially polarized cases have been proposed based on the theory of radar polarimetry. It is the purpose of this paper to present optimization procedures for the enhancement of polarimetric contrast between two time-varying targets and to extend the procedure to two spatially incoherent image pixel targets. The targets are now characterized by the time-averaged or spatially-averaged Kronecker matrices, from which one can obtain the associated Graves and Kennaugh matrices. The Graves matrices of the targets are used to find a transmitter polarization to maximize the ratio of scattered power densities at the receiver. Using the Lagrange multiplier method, the maximization problem is cast into the form of a generalized Balois eigenvalue equation. The largest eigenvalue of the equation equals the maximal power ratio, and the optimal effective length of the transmitting antenna is proportional to the corresponding eigenvector. The Kennaugh matrices of the targets are employed to obtain the Kennaugh vectors of partially polarized scattered waves from the two targets. Each of the scattered Kennaugh vectors is decomposed into a completely polarized and an unpolarized part. It is well known that the power received from the unpolarized part is independent of the polarization characteristics of the receiving antenna. Then a receiver polarization is selected to maximize or minimize the completely polarized part scattered from the desired or the undesired target. As a numerical example, the optimal Stokes vectors of transmitting and receiving antennas are given to show the validity of the optimization procedures and how it can be applied to perfecting high resolution POL-SAR/SAL Image Feature Extraction.