This paper presents a general result for the simulation of correlated heterogeneous targets, which are present in images corrupted by speckle noise. This technique is based on the use of a correlation mask and Gaussian random variables, in order to obtain spatially dependent Gamma deviates. These Gamma random variables, in turn, allow the obtainment of correlated 𝒦 deviates with specified correlation structure. The theoretical properties of the procedure are presented, along with the corresponding algorithm.