Learning from high-dimensional data is a classically difficult problem with the so-called “curse of dimensionality” being perhaps the most widely known symptom. So, e.g., classical approaches to covariance estimation require n>p where n is the number of observations of a p-dimensional vector. In practice, this is not practical if p is very large, as is often the case in image analysis problem. In this talk, we present a set of tools based on sparse transformations of high-dimensional data that are designed for both covariance estimation and processing of high-dimensional data. The methods are based on ML estimation of the covariance subject to a nonlinear sparsity constraint.