Nonlinear primal-dual method for total variation-based image restoration

Tony F. Chan, Gene H. Golub, Pep Mulet

Research output: Contribution to journalArticlepeer-review

659 Scopus citations


We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity |DELu| in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint, 1994] and Andersen [Ph.D. thesis, Odense University, Denmark, 1995] for the minimization of a sum of Euclidean norms. In addition to processing local quadratic convergence, experimental results show that the new method seems to be globally convergent.

Original languageEnglish (US)
Pages (from-to)1964-1977
Number of pages14
JournalUnknown Journal
Issue number6
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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