An Overview on Algorithms for Sparse Recovery

Sparsity is a very powerful prior for the identification of signals from noisy indirect measurements. The recovery of the signal is usually performed by suitable linearly constrained optimizations with additional sparsity enforcing barriers. Depending on the specific formulation, one can produce a variety of different algorithms. In this Chapter the numerical realizations of such linear and nonlinear programs are reviewed and compared with respect to different noisy scenarios. With the intention of providing a useful guide to users, we provide a sound mathematical introduction with rigorous derivations and proofs of convergence of all algorithms and we illustrate in detail their behavior by extensive numerical experiments.