Modeling high-resolution synthetic aperture radar images with heavy-tailed distributions

Statistical distributions of synthetic aperture radar SAR images based on central limit theorem cannot reflect the statistical characteristics of sharp peak and heavy tail of high-resolution SAR images. By using the generalized central limit theorem, the heavy-tailed distributions heavy-tailed Rayleigh distribution for amplitude image and heavy-tailed exponential distribution for intensity image are obtained from the symmetric stable distributions of real and imaginary parts of echoes. Taking the heavy-tailed Rayleigh distribution as an example, the algebraic tails of heavy-tailed distributions are explained as well as the statistical properties of sharp peak and heavy tail. In order to model the high-resolution SAR images with the heavy-tailed distributions, based on second-kind statistical, Characteristics the log-cumulant estimator is proposed to efficiently estimate the parameters of the heavy-tailed distributions. Modeling experiments on real SAR images demonstrate that the heavy-tailed distributions based on the generalized central limit theorem can accurately describe the sharp-peaked and heavy-tailed statistical characteristics of high-resolution SAR images.