Gradient-based algorithms with applications to signal-recovery problems

This chapter presents, in a self-contained manner, recent advances in the design and analysis of gradient-based schemes for specially structured, smooth and nonsmooth minimization problems. We focus on the mathematical elements and ideas for building fast gradient-based methods and derive their complexity bounds. Throughout the chapter, the resulting schemes and results are illustrated and applied on a variety of problems arising in several specific key applications such as sparse approximation of signals, total variation-based image-processing problems, and sensor-location problems.