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August  2009, 3(3): 487-503. doi: 10.3934/ipi.2009.3.487

Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm

Yingying Li 1, and  Stanley Osher 1,

1. 

UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, United States, United States

Received  February 2009 Revised  June 2009 Published  July 2009

We propose a fast algorithm for solving the Basis Pursuit problem, minu $\{|u|_1\: \Au=f\}$, which has application to compressed sensing. We design an efficient method for solving the related unconstrained problem minu $E(u) = |u|_1 + \lambda \||Au-f\||^2_2$ 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.
Keywords: Bregman iteration, Basis Pursuit, shrinkage, greedy sweep, constrained problem..
Mathematics Subject Classification: Primary: 90C25; Secondary: 65K0.
Citation: Yingying Li, Stanley Osher. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems and Imaging, 2009, 3 (3) : 487-503. doi: 10.3934/ipi.2009.3.487
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