The noncentral wishart distribution: properties and application to speckle imaging

Whereas central Wishart distributions have been extensively studied in the literature, the related noncentral distributions have received less attention. This paper studies interesting properties of these noncentral Wishart distributions such as closed form expressions for the moments. This work is motivated by the fact that this distribution plays a central part in the modeling of images corrupted by speckle. More precisely, the multivariate distribution of the intensity arising from a nonzero mean Gaussian wavefront amplitude is the diagonal of a noncentral Wishart distribution. Two examples which are interesting for synthetic aperture radar imaging and optical imaging through turbulence are discussed