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Bregman operator splitting with variable stepsize for total variation image reconstruction

Author

Listed:
  • Yunmei Chen
  • William Hager
  • Maryam Yashtini
  • Xiaojing Ye
  • Hongchao Zhang

Abstract

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form $\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$ , where ϕ 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. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yunmei Chen & William Hager & Maryam Yashtini & Xiaojing Ye & Hongchao Zhang, 2013. "Bregman operator splitting with variable stepsize for total variation image reconstruction," Computational Optimization and Applications, Springer, vol. 54(2), pages 317-342, March.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:2:p:317-342
    DOI: 10.1007/s10589-012-9519-2
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    References listed on IDEAS

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    1. Mingqiang Zhu & Stephen Wright & Tony Chan, 2010. "Duality-based algorithms for total-variation-regularized image restoration," Computational Optimization and Applications, Springer, vol. 47(3), pages 377-400, November.
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    Cited by:

    1. Maryam Yashtini, 2021. "Multi-block Nonconvex Nonsmooth Proximal ADMM: Convergence and Rates Under Kurdyka–Łojasiewicz Property," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 966-998, September.
    2. Jianchao Bai & William W. Hager & Hongchao Zhang, 2022. "An inexact accelerated stochastic ADMM for separable convex optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 479-518, March.
    3. Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
    4. William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.
    5. William W. Hager & Hongchao Zhang, 2020. "Convergence rates for an inexact ADMM applied to separable convex optimization," Computational Optimization and Applications, Springer, vol. 77(3), pages 729-754, December.

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