COORDINATE DESCENT OPTIMIZATION FOR l1 MINIMIZATION WITH APPLICATION TO COMPRESSED SENSING; A GREEDY ALGORITHM

We propose a fast algorithm for solving the Basis Pursuit problem, min(u) {vertical bar u vertical bar(1) : Au = f}, which has application to compressed sensing. We design an efficient method for solving the related unconstrained problem min(u) E(u) = vertical bar u vertical bar(1) + lambda parallel to Au - f parallel to(2)(2) based on a greedy coordinate descent method. We claim that in combination with a Bregman iterative method, our algorithm will achieve a solution with speed and accuracy competitive with some of the leading methods for the basis pursuit problem.