A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing

Yifei Lou, Tieyong Zeng, Stanley Osher, Jack Xin

Research output: Contribution to journalJournal articlepeer-review

153 Citations (Scopus)
22 Downloads (Pure)


We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods.

Original languageEnglish
Pages (from-to)1798-1823
Number of pages26
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - 10 Sept 2015

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Anisotropic TV
  • Bregman and split Bregman iterations
  • Convergence to stationary points
  • Difference of convex algorithm
  • Isotropic TV
  • Stable oscillatory errors
  • Weighted difference


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