Variational Approach for Restoring Blurred Images with Cauchy Noise

Federica Sciacchitano, Yiqiu Dong, Tieyong Zeng

Research output: Contribution to journalJournal articlepeer-review

58 Citations (Scopus)
20 Downloads (Pure)


The restoration of images degraded by blurring and noise is one of the most important tasks in image processing. In this paper, based on the total variation (TV) we propose a new variational method for recovering images degraded by Cauchy noise and blurring. In order to obtain a strictly convex model, we add a quadratic penalty term, which guarantees the uniqueness of the solution. Due to the convexity of our model, the primal dual algorithm is employed to solve the minimization problem. Experimental results show the effectiveness of the proposed method for simultaneously deblurring and denoising images corrupted by Cauchy noise. Comparison with other existing and well-known methods is provided as well.

Original languageEnglish
Pages (from-to)1894-1922
Number of pages29
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - 17 Sept 2015

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Cauchy noise
  • Image deblurring
  • Image denoising
  • Primal dual algorithm
  • Total variation regularization
  • Variational model


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