J4 ›› 2014, Vol. 41 ›› Issue (5): 141-147.doi: 10.3969/j.issn.1001-2400.2014.05.024

• Original Articles • Previous Articles     Next Articles

Nonconvex image inpainting via balanced regularization approach

WU Yulian1,2;FENG Xiangchu1   

  1. (1. School of Mathematics and Statistics, Xidian Univ., Xi'an  710071, China;
    2. Common Course Department, Xi'an Medical College, Xi'an  710021, China)
  • Received:2013-05-16 Online:2014-10-20 Published:2014-11-27
  • Contact: WU Yulian E-mail:wyl_wp711@163.com

Abstract:

Real images usually have two layers, namely, cartoons and textures, both of these layers have sparse approximations under some tight frame systems such as curvelet, local DCTs, and B-spline wavelet. In this paper, we solve the image inpainting problem by using two separate tight frame systems which can sparsely represent the two parts of the image. Different from existing schemes in the literature which are either analysis-based or synthesis-based sparsity priors, our minimization formulation applies the nonconvex sparsity prior via the balanced approach. We also derive iterative algorithms for finding their solutions. Numerical simulation examples are given to demonstrate that our proposed nonconvex method achieves significant improvements over the classical l1 sparse method and the variation TV method in image inpainting.

Key words: image inpainting, cartoons and textures, nonconvex, tight frame systems