Bregman operator splitting with variable stepsize for total variation image reconstruction

Document Type

Article

Publication Date

3-1-2013

Abstract

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form minphi(Bu)+1/2Au- 22, where may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related to the scheme used in SpaRSA (Sparse Reconstruction by Separable Approximation). Global convergence of the proposed BOSVS algorithm to a solution of the optimization problem is established. BOSVS is compared with other operator splitting schemes using partially parallel magnetic resonance image reconstruction problems. The experimental results indicate that the proposed BOSVS algorithm is more efficient than the BOS algorithm and another split Bregman Barzilai-Borwein algorithm known as SBB. © 2012 Springer Science+Business Media New York.

Publication Source (Journal or Book title)

Computational Optimization and Applications

First Page

317

Last Page

342

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