IRLS Based Algorithm for Signal Recovery from Noisy Compressive Measurements

Abstract

Compressive Sensing (CS) is a novel theory states that sparse signals can be recovered from only a few measurements far below that dictated by the Nyquist sampling theorem. To recover the signal, one needs to find the sparse solution to an under-determined linear system. When the measurements are contaminated by noise, an unconstrained minimization problem is often considered. Since it is NP hard to solve, we try to solve an approximation using an Iterative Re- weighted Least Square (IRLS) algorithm. We discuss the convergence properties of this algorithm and provide several numerical results. Our algorithm is robust in the presence of noise and capable of recovering signals that are less sparse than possible with the best alternate approaches.