Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0025-5718-09-02242-X
Title: Convergence of the linearized Bregman iteration for ℓ1-norm minimization
Authors: Cai, J.-F. 
Osher, S.
Shen, Z. 
Issue Date: Oct-2009
Citation: Cai, J.-F., Osher, S., Shen, Z. (2009-10). Convergence of the linearized Bregman iteration for ℓ1-norm minimization. Mathematics of Computation 78 (268) : 2127-2136. ScholarBank@NUS Repository. https://doi.org/10.1090/S0025-5718-09-02242-X
Abstract: One of the key steps in compressed sensing is to solve the basis pursuit problem min urnu1: Au=f. Bregman iteration was very successfully used to solve this problem in [40]. Also, a simple and fast iterative algorithm based on linearized Bregman iteration was proposed in [40], which is described in detail with numerical simulations in [35]. A convergence analysis of the smoothed version of this algorithm was given in [11]. The purpose of this paper is to prove that the linearized Bregman iteration proposed in [40] for the basis pursuit problem indeed converges. © 2009 American Mathematical Society.
Source Title: Mathematics of Computation
URI: http://scholarbank.nus.edu.sg/handle/10635/115657
ISSN: 00255718
DOI: 10.1090/S0025-5718-09-02242-X
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