Primal-dual algorithms for total variation based image restoration under Poisson noise

You Wei WEN*, Raymond Honfu CHAN, Tie Yong ZENG

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

51 Citations (Scopus)


We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler (KL)-divergence term for the Poisson noise and a total variation (TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers (ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock’s first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.

Original languageEnglish
Pages (from-to)141-160
Number of pages20
JournalScience China Mathematics
Issue number1
Early online date5 Nov 2015
Publication statusPublished - Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, Science China Press and Springer-Verlag Berlin Heidelberg.


  • alternating direction method of multipliers (ADMM)
  • image restoration
  • minimax problem
  • Poisson noise
  • primal-dual
  • total variation (TV)


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