The analysis of Synthetic Aperture Radar (SAR) imagery is an important step in remote sensing applications, and it is a challenging problem due to its inherent speckle noise. One typical solution is to model the data using the $G_{I}^{0}$ distribution and extract its roughness information, which in turn can be used in posterior imaging tasks, such as segmentation, classification and interpretation. This leads to the need for quick and reliable estimation of the roughness parameter from SAR data, especially with high-resolution images. Unfortunately, traditional parameter estimation procedures are slow and prone to estimation failures. In this work, we proposed a neural network-based estimation framework that first learns how to predict the underlying parameters of $G_{I}^{0}$ samples and then can be used to estimate the roughness of unseen data. We show that this approach leads to an estimator that is quicker, yields less estimation error, and is less prone to failures than the traditional estimation procedures for this problem, even when we use a simple network. More importantly, we show that this same methodology can be generalized to handle image inputs and, even if trained on purely synthetic data for a few seconds, is able to perform real-time pixel-wise roughness estimation for high-resolution real SAR imagery.