2310543 – Compressed Sensing and Approximate Message Passing: Theory and Applications
This course covers compressed sensing (CS) and approximate message passing (AMP), two powerful frameworks at the intersection of signal processing, statistical inference, and optimization. Starting from the fundamentals of sparse signal recovery, the course introduces students to key concepts in high-dimensional statistics, signal processing and Bayesian inference that underlie CS and AMP. Special attention will be given to the AMP algorithm and its variants, which provide an iterative solution to a wide set of linear inverse problems.
Topics include: Sparsity and underdetermined linear systems, Convex and greedy recovery algorithms (e.g., Basis Pursuit, Orthogonal Matching Pursuit), Introduction to high-dimensional probability and random matrices, Approximate message passing, Bayesian CS and inference in graphical models, Applications in imaging, communications, and machine learning.