The multilinear compound Gaussian distribution

We introduce a novel generalization of the compound Gaussian (CG) (or Gaussian Scale Mixture [1]) distribution which extends the Gaussian component of the CG model to a multilinear distribution. The resulting model, which we call the Multilinear Compound Gaussian (MCG) distribution, subsumes both GSM [1] and the previously developed MICA [3-4] distributions as complementary special cases; thereby allowing us to model a richer class of stochastic phenomena. First we derive the structural characterization of the MCG distribution and develop some of its important theoretical properties. Thereafter we describe a parameter estimation algorithm for learning this model from sample data, and then deploy this for modeling textures, including natural (i.e. optical) and SAR images. Our simulation results demonstrate how, for each case, we obtain improved performance over the CG model; thus indicating the versatility of the MCG model in accurately modeling various natural phenomena of interest.