An Improved LOT Model for Image Restoration

  • Authors:

  • Fangfang Dong;Zhen Liu;Dexing Kong;Kefeng Liu

  • Affiliations:

  • Center of Mathematical Sciences, Zhejiang University, Hangzhou, China 310027;Center of Mathematical Sciences, Zhejiang University, Hangzhou, China 310027 and Department of Mathematics, Zhejiang University of Technology, Hangzhou, China 310023;Department of Mathematics, Zheijiang University, Hangzhou, China 310027;Center of Mathematical Sciences, Zhejiang University, Hangzhou, China 310027

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2009

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Abstract

Some second order PDE-based image restoration models such as total variation (TV) minimization or ROF model of Rudin et al. (Physica D 60, 259–268, 1992) can easily give rise to staircase effect, which may produce undesirable blocky image. LOT model proposed by Laysker, Osher and Tai (IEEE Trans. Image Process. 13(10), 1345–1357, 2004) has alleviated the staircase effect successfully, but the algorithms are complicated due to three nonlinear second-order PDEs to be computed, besides, when we have no information about the noise, the model cannot preserve edges or textures well. In this paper, we propose an improved LOT model for image restoration. First, we smooth the angle θ rather than the unit normal vector n, where n=(cos θ,sin θ). Second, we add an edge indicator function in order to preserve fine structures such as edges and textures well. And then the dual formulation of TV-norm and TV g -norm are used in the numerical algorithms. Finally, some numerical experiments prove our proposed model and algorithms to be effective.