The L_A Distribution: An Approximation of the G⁰_A Distribution for Amplitude SAR Image Modeling

This article introduces a continuous probability distribution as an approximation to the ${\mathcal {G}}^{0}_{A}$ distribution for amplitude synthetic aperture radar (SAR) imagery modeling. Called ${\mathcal {L}}_{A}$ distribution, it is an empirical model and an analytically more tractable alternative than ${\mathcal {G}}^{0}_{A}$ 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 ${\mathcal {L}}_{A}$ 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 ${\mathcal {L}}_{A}$ instead of ${\mathcal {G}}^{0}_{A}$ 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 ${\mathcal {G}}^{0}_{A}$ and ${\mathcal {L}}_{A}$ 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 ${\mathcal {L}}_{A}$ distribution in all considered cases and figure-of-metrics.