A Convex Variational Model for Restoring Blurred Images with Large Rician Noise

Liyuan Chen, Tieyong ZENG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

26 Citations (Scopus)


In this paper, a new convex variational model for restoring images degraded by blur and Rician noise is proposed. The new method is inspired by previous works in which the non-convex variational model obtained by maximum a posteriori estimation has been presented. Based on the statistical property of Rician noise, we put forward to adding an additional data-fidelity term into the non-convex model, which leads to a new strictly convex model under mild condition. Due to the convexity, the solution of the new model is unique and independent of the initialization of the algorithm. We utilize a primal–dual algorithm to solve the model. Numerical results are presented in the end to demonstrate that with respect to image restoration capability and CPU-time consumption, our model outperforms some of the state-of-the-art models in both medical and natural images.

Original languageEnglish
Pages (from-to)92-111
Number of pages20
JournalJournal of Mathematical Imaging and Vision
Issue number1
Publication statusPublished - 3 Sept 2015

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

User-Defined Keywords

  • Convexity
  • Deblurring
  • Primal–dual method
  • Rician noise
  • Total variation


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