Poisson modulated stochastic model for partially developed multi-look speckle

Abstract

Biological tissues of physiological systems have different characteristics. As a result, tissues imaged by ultrasound systems have varying degrees of "roughness" with respect to the wavelength of the illuminating radiation. This roughness can be modeled in terms of the locations of the individual elemental scatterers or scattering centers that contribute to the ultrasound backscatter from the tissue. When the number of scatterers within a tissue is very large and the scatterers' distribution occurs on a scale of a wavelength or greater, the speckle is referred to as fully developed. However, many tissue structures have a relatively small number of dominant scatterers within the imaged region. In this case, when the imaged tissue is smooth on the scale of a wavelength, speckle is referred to as partially developed and it can carry useful information about the scattering tissue. In this paper, we derive stochastic models for partially developed multi-look speckle noise. The motivation for this work is the problem of segmentation and tissue classification using ultrasound imaging. Modeling of speckle in this context involves an underlying Poisson point process which modulates a Gram-Charlier series of generalized Laguerre weighted gamma functions, resulting in a doubly stochastic marked accumulator Poisson point process. It is observed that as the mean number of scatterers in a resolution cell or the number of looks is increased, the probability density function of speckle intensity approaches a gamma distribution. This is consistent with fully developed speckle noise as dictated by the Central Limit theorem.