Abstract
A new PCA-based method for an optimal representation of multi-frequency polarimetric SAR images is proposed. The method performs the simultaneous diagonalization of the signal and multiplicative noise covariance matrices via one orthogonal matrix. The covariance matrix of the multiplicative noise becomes an identity matrix, which implies that the variance of the noise in each new image is unity, and is uncorrelated between transformed images. The covariance matrix of the SAR images is transformed to a diagonal matrix whose diagonal elements are ordered in decreasing value, which means that the new images are uncorrelated and will be ordered by their variances (qualities). The theoretical analysis and the implementation procedure of the method are given. The method has been applied on real SAR images. The compression ability of the method is proved via a reconstitution process of the original SAR images from a small number of new images with a minimal loss of information.