Duality-based algorithms for total-variation-regularized image restoration

Mingqiang Zhu, Stephen J. Wright, Tony F. Chan

Research output: Contribution to journalArticlepeer-review

116 Scopus citations


Image restoration models based on total variation (TV) have become popular since their introduction by Rudin, Osher, and Fatemi (ROF) in 1992. The dual formulation of this model has a quadratic objective with separable constraints, making projections onto the feasible set easy to compute. This paper proposes application of gradient projection (GP) algorithms to the dual formulation.We test variants of GP with different step length selection and line search strategies, including techniques based on the Barzilai-Borwein method. Global convergence can in some cases be proved by appealing to existing theory. We also propose a sequential quadratic programming (SQP) approach that takes account of the curvature of the boundary of the dual feasible set. Computational experiments show that the proposed approaches perform well in a wide range of applications and that some are significantly faster than previously proposed methods, particularly when only modest accuracy in the solution is required.

Original languageEnglish (US)
Pages (from-to)377-400
Number of pages24
JournalComputational Optimization and Applications
Issue number3
StatePublished - Nov 2010
Externally publishedYes


  • Constrained optimization
  • Gradient projection
  • Image denoising

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Duality-based algorithms for total-variation-regularized image restoration'. Together they form a unique fingerprint.

Cite this