The L-A Distribution: An Approximation of the G(A)(0) Distribution for Amplitude SAR Image Modeling

This article introduces a continuous probability distribution as an approximation to the G(A)(0) distribution for amplitude synthetic aperture radar (SAR) imagery modeling. Called L-A distribution, it is an empirical model and an analytically more tractable alternative than G(A)(0) model, with the same number of parameters and no special functions in its formulation. It also has a closed form for the quantile function, making it easier to calculate quantiles and generate pseudorandom numbers and obtain closed-form expressions for skewness and kurtosis coefficients. Useful properties of the LA distribution are introduced, and the maximum likelihood method is considered for parameter estimation. Based on the Kullback-Leibler divergence (KLD), it is shown that the average information missed when using the LA instead of G(A)(0) distribution is negligible. Numerical studies in simulated and measured SAR images obtained by different systems and representing different land-use regions are conducted to compare the performances of the G(A)(0) and LA distributions. The simulation results suggest that the parameter estimation performances of both distributions are similar. Applications to real data show that the images were best fit with the LA distribution in all considered cases and figure-of-metrics.