Non-Gaussian versus non-Rayleigh statistical properties of ultrasound echo signals

Parameters expressing the non-Gaussian and the non-Rayleigh properties of ultrasound echo signals are derived for the case of a pulsed transducer insonifying a medium containing randomly distributed scatterers. Both parameters depend on the measurement system, including the transducer field and pulse frequency content, as well as on the medium's properties. The latter is expressed in terms of the number of scatterers per unit volume and the second and fourth moments of the medium's scattering functions. A simple relationship between the parameters describing the non-Gaussian and non-Rayleigh properties is derived and verified experimentally.>