Sparse stochastic processes are continuous time stochastic models for sparse signals. It has been shown that such processes are limit points (in distribution) of a sequence of compound Poisson processes, which are roughly a random sum of Dirac impulses that each have independent random heights. The goal of this project is to use this theoretical observation in order to generate sparse stochastic processes with arbitrary accuracy. It requires a theoretical understanding of the convergence with some bounds guaranteeing the accuracy of the generated process. This project will also include an implementation that can be used to model natural signals and images. The student should have a solid understanding of functional analysis and probability theory, and basic knowledge of programming.