Greedy minimization of l₁-norm with high empirical success

Abstract

We develop a greedy algorithm for the basis-pursuit problem. The algorithm is empirically found to provide the same solution as convex optimization based solvers. The method uses only a subset of the optimization variables in each iteration and iterates until an optimality condition is satisfied. In simulations, the algorithm converges faster than standard methods when the number of measurements is small and the number of variables large.