Speckle ensemble statistics of logarithmically scaled data [radar]

It is shown that statistics of logarithmically scaled (averaged) radar data can be described by simple analytical expressions using Riemann´s zeta function and Eule´s psi function. This achievement makes possible the proper qualification of the impact of such transformation on the physical interpretation of remote sensing data and derived data (i.e. field-averaged mean and standard deviation). The standard deviation for Rayleigh-fading objects is a constant at a logarithmic scale and depends on the number k only. Averaging at a logarithmic scale of radar data, which themselves result from the linear averaging over k independent samples or looks, introduces an offset dependent on the number k only. This offset does not depend on the mean level of the signal and therefore is the same for all Rayleigh-fading objects in the scene