An efficient method for compressed sensing

Compressed sensing or compressive sampling (CS) has been receiving a lot of interest as a promising method for signal recovery and sampling. CS problems can be cast as convex problems, and then solved by several standard methods such as interior-point methods, at least for small and medium size problems. In this paper we describe a specialized interior-point method for solving CS problems that uses a preconditioned conjugate gradient method to compute the search step. The method can efficiently solve large CS problems, by exploiting fast algorithms for the signal transforms used. The method is demonstrated with a medical resonance imaging (MRI) example.