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

Abstract

Abstract-In this paper, the use of the l2-norm, or Span, of the scattering vectors is suggested to texture analysis of PolSAR data, with the benefits that neither we need to analyze the polarimetric channels separately, nor a filtering of the data is required to analyze the statistics. Based on the product model, the distribution of the l2-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 l2-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 the statistics based on the l2-norm brings advantages in several aspects with respect to the normalized intensity moments and matrix variate log-cumulants.

Statistical Modeling of Polarimetric SAR Data: A Survey and Challenges

“…In SAR or PolSAR images, it is also found to be useful to distinguish different target types. For example, trees of different heights can be distinguished by texture information [73]. However, currently the most common way to make use of texture models is to design probability based algorithms (e.g., classification and segmentation) by replacing the Gaussian distribution or the Wishart distribution [4][5][6].…”

“…However, we need to filter the data (the multilook process) to obtain the sample covariance matrices, which could change the actual statistical properties of the data. To overcome these problems, the l 2 -norms of the scattering vectors can be employed, and they are found to be a useful tool for texture analysis of PolSAR data [73]. However, there are also limitations, e.g., the difference between models are not very large.…”