Adapted statistical compressive sensing: Learning to sense gaussian mixture models

A framework for learning sensing kernels adapted to signals that follow a Gaussian mixture model (GMM) is introduced in this paper. This follows the paradigm of statistical compressive sensing (SCS), where a statistical model, a GMM in particular, replaces the standard sparsity model of classical compressive sensing (CS), leading to both theoretical and practical improvements. We show that the optimized sensing matrix outperforms random sampling matrices originally exploited both in CS and SCS.