A new constrained total variational deblurring model and its fast algorithm

Bryan Michael Williams, Ke Chen, Simon P. Harding

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
1 Downloads (Pure)


Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.

Original languageEnglish
Pages (from-to)415-441
Number of pages27
JournalNumerical Algorithms
Issue number2
Early online date21 Feb 2015
Publication statusPublished - 30 Jun 2015
Externally publishedYes


  • alternating direction method of multipliers
  • box constraint
  • image deblurring
  • total variation
  • transforms


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