A Statistical Central Moment Approach to Super-Resolved Multiparameter Scatter Characterization

We propose a paradigm shift in the conceptual framing of the sub-resolution problem for distributed, non-sparse scatterers - moving from imaging to statistical characterization of the scatter distribution. While traditional techniques fail for targets smaller than the classical resolution limit (c/2B), our approach estimates the scatterer's central moments to determine its physical location (mean), size (variance), asymmetry (skewness), and central density (kurtosis). We demonstrate this by training a neural network to accurately predict these moments from polynomial coefficients fitted to the noisy return signal. Results show high accuracy in multiparameter characterization, even when the entire scatter distribution is significantly smaller than the signal's inverse bandwidth, offering a new path to super-resolved analysis.