A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope

In ultrasound imaging, various statistical distributions have been proposed to model the first-order statistics of the amplitude of the echo envelope. We present an overview of these distributions based on their compound representation, which comprises three aspects: the modulated distribution (Rice or Nakagami); the modulating distribution (gamma, inverse Gaussian or even generalized inverse Gaussian); and the modulated parameters (the diffuse signal power with or without the coherent signal component or the coherent signal power). This unifying point of view makes the comparison of the various models conceptually easier. In particular, we discuss the implications of the modulated parameters on the mean intensity and the signal-to-noise ratio of the intensity in the case of a vanishing diffuse signal. We conclude that the homodyned K-distribution is the only model among the literature for which the parameters have a physical meaning that is consistent with the limiting case, although the other distributions may fit real data.