Cauchy Noise Removal by Nonconvex ADMM with Convergence Gaurantees

Jin-Jin Mei, Yiqiu Dong, Ting-Zhu Huang, Wotao Yin

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Image restoration is one of the most important and essential issues in image processing. Cauchy noise in engineering application has the non-Gaussian and impulsive property. In order to preserve edges and details of images, the total variation (TV) based variational model has been studied for restoring images degraded by blur and Cauchy noise. Due to the nonconvexity and nonsmoothness, there exist computational and theoretical challenges. In this paper, adapting recent results, we develop an alternating direction method of multiplier (ADMM) in spite of the challenges. The convergence to a stationary point is guaranteed theoretically under certain conditions. Experimental results demonstrate that the proposed method is competitive with other methods in terms of visual and quantitative measures. Especially, by comparing to the PSNR values, our method can improve about 0.5dB on average.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages24
Publication statusPublished - 2016
SeriesDTU Compute-Technical Report-2016


  • Nonconvex variational model
  • Image restoration
  • Total variation
  • Alternating direction method of multiplier
  • Kurdyka-Łojasiewicz

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