Principal Component Analysis (PCA) in Radar Polarimetry

Abstract

Statistical and computational techniques for revealing the internal structure that underlies the set of random correlated data exists in a great variety at present, and target decomposition theorems, either in the coherent or incoherent formulation, are well established. In spite of this fact a rather innovative and new concept is presented in this contribution which was proposed for radar polarimetry by late Dr. Ernst Lüneburg. In turn the Principal Component Analysis is considered to possibly add value to existing approaches, and it allows for an interpretation of polarimetric synthetic aperture radar measurements using variables obtained via linear transformation. Starting with the Sinclair backscatter matrix which will be further transformed into the so called target feature vector by stacking column elements of S and generating the covariance matrices averaged over a certain pixel array we show, how the Sinclair backscatter matrix is decomposed into the sum of a maximum of four 2 x 2 elementary point scatter matrices which are weighted by the principal components, whereas the variances of this components agree with the eigenvalues of the covariance matrix. In conclusion this mathematical development defines a decomposition which expresses scattering mechanism from distributed targets in terms of scattering matrices via an incoherent step.