  Synthetic Aperture Radar (SAR) image understanding is crucial in remote
sensing applications, but it is hindered by its intrinsic noise contamination,
called speckle. Sophisticated statistical models, such as the $\mathcal{G}^0$
family of distributions, have been employed to SAR data and many of the current
advancements in processing this imagery have been accomplished through
extracting information from these models. In this paper, we propose
improvements to parameter estimation in $\mathcal{G}^0$ distributions using the
Method of Log-Cumulants. First, using Bayesian modeling, we construct that
regularly produce reliable roughness estimates under both $\mathcal{G}^0_A$ and
$\mathcal{G}^0_I$ models. Second, we make use of an approximation of the
Trigamma function to compute the estimated roughness in constant time, making
it considerably faster than the existing method for this task. Finally, we show
how we can use this method to achieve fast and reliable SAR image understanding
based on roughness information.
