A Family of Measurement Matrices for Generalized Compressed Sensing

Explore a comprehensive lecture on generalized compressed sensing, focusing on a family of measurement matrices for recovering structured signals. Delve into the problem of reconstructing signals close to a subset of interest in R^n from random noisy linear measurements. Examine how varying the fixed matrix B and the sub-gaussian distribution of A creates a diverse family of measurement matrices with unique properties. Investigate the role of the "effective rank" of B as a surrogate for the number of measurements and its relationship to the Gaussian complexity of the subset T. Learn about the optimal dependence on the sub-gaussian norm of A's rows and its implications for signal recovery. Apply these concepts to low-rank matrix recovery scenarios and explore topics such as robust recovery, testing matrices, universality, and restricted isometries.