A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

  • Authors:

  • Dai-Qiang Chen;Hui Zhang;Li-Zhi Cheng

  • Affiliations:

  • Department of Mathematics and System, School of Sciences, National University of Defense Technology, Changsha, P.R. China 410073;Department of Mathematics and System, School of Sciences, National University of Defense Technology, Changsha, P.R. China 410073;Department of Mathematics and System, School of Sciences, National University of Defense Technology, Changsha, P.R. China 410073

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2012

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Abstract

In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.