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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 + \||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.
Li et al. (Thu,) studied this question.