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Coordinate descent optimization for \(l^{1}\) minimization with application to compressed sensing; a greedy algorithm. (English) Zbl 1188.90196

Summary: 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.

MSC:

90C25 Convex programming
65K05 Numerical mathematical programming methods
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