Compressed Sensing and Sparse Signal Recovery - Theory and Applications

Compressed sensing is a technique for efficiently acquiring a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the signal can be recovered from far fewer samples than required by the Nyquist-Shannon sampling theorem. The lecture will focus on (a) Orthogonal Matching Pursuit (OMP) algorithm and its variations to recover any signal compared to other convex optimization approaches with respect to performance and convergence, (b) the dictionary learning problem based on Gaussian Mixture Models (GMM) and structured sparsity, and (c) different applications with respect to blind source separation and image inpainting.