Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

We establish in the world of stochastic processes a theoretical relation between sparsity and wavelets. The underlying principle is to treat stochastic processes as generalized functions, which facilitates the study of their properties in a transform domain. We focus on symmetric-$\alpha$-stable (S$\alpha$S) processes, with $\alpha\in(0,2]$. They are central to a recently proposed framework for sparse stochastic processes. The case $0