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We propose a fast algorithm for solving the Basis Pursuit problem, min u $\{|u|_1\: \Au=f\}$, which has application to compressed sensing. We design an efficient method for solving the related unconstrained problem min u $E(u) = |u|_1 + \lambda \||Au-f\||^2_2$ 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.

inverse problems and imaging

Coordinate descent optimization for &lt;i&gt;l&lt;/i&gt;&lt;SUP&gt;1&lt;/SUP&gt; minimization with application to compressed sensing; a greedy algorithm