Box constrained total generalized variation model and primal-dual algorithm for Poisson noise removal

  • Yehu LvEmail author
  • Xinwei Liu


We consider the image denoising problem under Poisson noise. To further enhance the image denoising effect, a box constraint is incorporated into the total generalized variation (TGV) model by simply projecting all pixel values of the denoised image to lie in a certain interval (e.g., [0, 1] for normalized images and [0, 255] for 8-bit images). Thus, a box constrained TGV model is proposed. Computationally, combining with the dual representation of the second-order TGV regularization, our proposed model is transformed into a minimax problem, and the Chambolle–Pock’s first-order primal-dual algorithm is used to compute the saddle point of the minimax problem. In addition, the convergence of Algorithm 1 is discussed. Numerical experiments demonstrate that our proposed model not only gets better visual effects but also obtains higher signal-to-noise ratio, peak signal-to-noise ratio and structural similarity index than several existing state-of-the-art methods.


Image denoising Poisson noise Total generalized variation (TGV) Box constraint Primal-dual algorithm 

Mathematics Subject Classification

35-XX 49-XX 68-XX 



This work was supported by the National Natural Science Foundation of China under Grant No. 11271107 and the Natural Science Foundation of Hebei Province of China under Grant No. A2015202365.


This study was funded by the National Natural Science Foundation of China (11271107) and the Natural Science Foundation of Hebei Province of China (A2015202365).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest, whether financial or non-financial.

Human participants

This research did not involve human participants and animals.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsHebei University of TechnologyTianjinChina

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