Generation of non-Rayleigh speckle distributions using marked regularity models

Fully developed speckle patterns observed in coherent imagery are character ized by a Rayleigh-distributed envelope amplitude. Non-Rayleigh distributio ns are observed in many cases, such as when the number of scatterers in a r esolution cell is small or scatterers are organized with some periodicity. Distributions resulting from the assumption of random scatterer phase (rand om walk models) have been used to describe the speckle amplitude in these c ases, leading to K, Rician, and homodyned-K amplitude distributions. An alt ernative is to incorporate non random phase implicitly by adopting models t hat directly describe the spatial placement of point scatterers. We examine the consequences of assuming that scattering is described in one dimension by a stationary renewal process in which the arrival times are the locatio ns of ideal point scatterers, the interscatterer distances are drawn from a gamma distribution, and the scatterer amplitudes are allowed to be correla ted in space. This model has been called the marked regularity model becaus e variations of the model parameters can generate spatial distributions ran ging from clustered to random to nearly periodic. We will demonstrate that all of the non-Rayleigh distributions generated by the previous random phas e models can also be generated by the marked regularity model, and we show under what conditions the different distributions will result. We also demo nstrate that the regularity model is inherently capable of describing certa in sparse scattering conditions. Therefore, the model can represent many ca ses and provide an intuitively pleasing description of the spatial placemen t of the scatterers.