A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems

In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend a primal-dual Newton Conjugate Gradients (pdNCG) method for CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results are presented on CS problems which demonstrate the performance of pdNCG with the proposed preconditioner compared to state-of-the-art existing solvers.