On Fractional Moments of Multilook Polarimetric Whitening Filter for Polarimetric SAR Data

Many multivariate statistical distributions have been derived using the well-known product model to stochastically model polSAR data. One important factor in their utilization is the estimation of their texture parameters. Recently, it has been shown that the method of matrix log cumulants (MoMLC) for multilook PolSAR statistical distributions results in estimators with low bias and variance properties. This method is becoming increasingly popular and can be regarded as state of the art. However, some distributions (e.g., G distribution) do not have closed-form MLC expressions, making the application of MoMLC a challenge. It is therefore desirable to have alternative parameter estimation methods. In this paper, we propose a new estimation method based on fractional moments of the multilook polarimetric whitening filter (MPWF). This results in estimators with mean square error that is even lower than the MoMLC-based estimators. In addition, the mathematical expressions of the estimators are computationally less complicated than MoMLC-based estimators. The proposed estimators can be easily derived for all commonly occurring multilook PolSAR distributions but have been only given for G, K, and G⁰ distributions in this paper. Comparisons are made with other known estimators for these distributions using simulated and real PolSAR data. For real data, formal goodness-of-fit testing, which is based on MLCs, has been used to assess the fitting accuracy of G, K, and G⁰ models using different estimators.