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.

Intro
Outline
General Theory
Robust Recovery
Testing matrices
Universality
Subgaussian
Random matrices
Subgaussian matrices
Example
Restricted isometries