A Family of Measurement Matrices for Generalized Compressed Sensing

This course aims to teach the learning outcomes and goals of recovering structured signals from random noisy linear measurements in a generalized compressed sensing framework. It covers the concept of a family of measurement matrices with varying properties, such as heavy tails and dependent rows, to understand the properties that enable accurate signal recovery. The course teaches the use of the "effective rank" of the measurement matrix as a surrogate for the number of measurements needed for recovery. The teaching method includes theoretical discussions, analysis of robust recovery, testing matrices, and exploring the universality of subgaussian and random matrices. The course is intended for individuals interested in advanced topics in compressed sensing, particularly those focusing on low-rank matrix recovery.