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

Yingying Li; Stanley Osher

doi:10.3934/ipi.2009.3.487

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2009, Volume 3, Issue 3: 487-503. Doi: 10.3934/ipi.2009.3.487 open access

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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

Received: February 2009

Revised: June 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C25; Secondary: 65K05.

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