Optimal inference of the inverse Gamma texture for a compound-Gaussian clutter

We first derive the stochastic dynamics of a Gaussian-compound model with an inverse gamma distributed texture from Jakeman´s random walk model with step number fluctuations. Following a similar approach existing for the K-distribution, we show how the scattering cross-section may be inferred from the fluctuations of the scattered field intensity. By discussing the sources of discrepancy arising during this process, we derive an analytical expression for the inference error based on its asymptotic behaviours, together with a condition to minimize it. Simulated data enables verification of our proposed technique. The interest of this strategy is discussed in the context of radar applications.