Non-smoothness and Compressive Sensing

This lecture covers the deficiency of smooth models in signal estimation, introducing sparsity and compressive sensing as solutions. It explores non-smooth minimization techniques, such as subgradient descent, and their applications in statistical learning, like linear regression. The lecture delves into the challenges of non-smooth optimization, emphasizing the importance of sparse representations and compressible signals. It discusses the practical performance of estimators, the impact of noise in linear models, and the concept of compressible signals. The lecture presents approaches for sparse signal recovery, including the Lasso optimization problem, and generalization via simple representations using atomic sets and atoms. Various models beyond sparsity are also introduced.