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, minu\|u|₁\: =f\, which has application to compressed sensing.We design an efficient method for solving the related unconstrained problem minu E(u) = |u|₁ + λ \||Au-f\||²₂ based on a greedy coordinate descentmethod. We claim that in combination with a Bregman iterative method, ouralgorithm will achieve a solution with speed and accuracy competitive with someof the leading methods for the basis pursuit problem.