On the Use of the $l_{2}$-Norm for Texture Analysis of Polarimetric SAR Data

In this paper, the use of the l
₂
-norm, or Span, of the scattering vectors is suggested for texture analysis of polarimetric synthetic aperture radar (SAR) data, with the benefits that we need neither an analysis of the polarimetric channels separately nor a filtering of the data to analyze the statistics. Based on the product model, the distribution of the l
₂
-norm is studied. Closed expressions of the probability density functions under the assumptions of several texture distributions are provided. To utilize the statistical properties of the l
₂
-norm, quantities including normalized moments and log-cumulants are derived, along with corresponding estimators and estimation variances. Results on both simulated and real SAR data show that the use of statistics based on the l
₂
-norm brings advantages in several aspects with respect to the normalized intensity moments and matrix variate log-cumulants.