MAXIMUM-LIKELIHOOD-ESTIMATION OF K-DISTRIBUTION PARAMETERS FOR SAR DATA

The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the Ii distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. In this paper, we apply a maximum likelihood estimation method directly to the K distribution. We consider the situation for single look SAR data as well as a simplified model for multilook data. We investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. We find improved results compared with those obtained by the method of moments for sample sizes of 1000 or less. We also compare our results with those from a new method given by Raghavan and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, we compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. We find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non Rayleigh. We note that the distributions for our data set differ too little between ice types to allow discrimination based on differing distribution parameters.