Mixture approximation to the amplitude statistics of isotropic α-stable clutter

The α-stable distribution has been recently adopted in modeling the clutter of synthetic aperture radar (SAR) images. However, α-stable clutter does not have analytical probability density function (PDF) except for a few special cases, and thus it is even harder to obtain the analytical amplitude PDF (APDF) for α-stable clutter. In this paper, an analytical representation is developed to approximate the APDF of isotropic α-stable clutter. In the approximation, the APDFs of Cauchy and Gaussian clutters are used as two linearly mixing components. In addition, four approaches are presented to compute the component weight. The proposed approximation has a concise closed-form, and its validity is verified by experimental results.