A fast and accurate first-order algorithm for compressed sensing

This paper introduces a new, fast and accurate algorithm for solving problems in the area of compressed sensing, and more generally, in the area of signal and image reconstruction from indirect measurements. This algorithm is inspired by recent progress in the development of novel first-order methods in convex optimization, most notably Nesterov´s smoothing technique. In particular, there is a crucial property that makes these methods extremely efficient for solving compressed sensing problems. Numerical experiments show the promising performance of our method to solve problems which involve the recovery of signals spanning a large dynamic range.