Generation of non-Rayleigh speckle distributions using regularity models [medical ultrasound]

Fully-developed speckle patterns observed in coherent imagery are characterized by a Rayleigh-distributed envelope amplitude. Non-Rayleigh distributions are observed in many cases, such as when the number of scatterers in a resolution cell is small, or scatterers are organized with some periodicity. K, Rician and homodyned-K distributions have all been used to model the speckle amplitude in these cases. We examine the consequences of assuming that scattering can be described in one dimension by a stationary renewal process in which the arrival times are the locations of ideal point scatterers and the interscatterer distances are drawn from a gamma distribution. This model has been called the “regularity model” because variations of the model parameters can generate spatial distributions ranging from clustered to random to periodic, so the model is therefore capable of describing structures in which scatterers are regularly (but nondeterministically) spaced. The mean interscatterer distance, the model order and the resolution cell size are the fundamental model parameters. We demonstrate that various non-Rayleigh distributions can be generated by an appropriate choice of parameters. The model can therefore represent many cases while providing an intuitively pleasing description of the spatial placement of the scatterers