Lossless and Sufficient $\Psi$ -Invariant Decomposition of Random Reciprocal Target

The target coherency or covariance matrices are the main operators useful for characterizing the polarization transformation properties of radar target by modeling the depolarization effect. In this paper, a novel decomposition of the target coherency matrix is proposed, that is sufficient for representing the physical characteristics of the observed medium in term of a minimum set of orientation invariant parameters. The Einstein's photon circular polarization basis is used for obtaining an orientation invariant physical interpretation of the proposed parameter set both for deterministic and random target. A generalized unsupervised classification scheme is also proposed for underlining the effectiveness of the proposed decomposition theorem for classifying random reciprocal target into 75 physically meaningful clusters. The application of the proposed decomposition theorem and classification algorithm is useful for developing of novel Remote Sensing products and Data Mining softwares for monitoring the surfaces of the Earth and the Moon.