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Fixed point algorithm based on adapted metric method for convex minimization problem with application to image deblurring

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Abstract

Recently, optimization algorithms for solving a minimization problem whose objective function is a sum of two convex functions have been widely investigated in the field of image processing. In particular, the scenario when a non-differentiable convex function such as the total variation (TV) norm is included in the objective function has received considerable interests since many variational models encountered in image processing have this nature. In this paper, we propose a fast fixed point algorithm based on the adapted metric method, and apply it in the field of TV-based image deblurring. The novel method is derived from the idea of establishing a general fixed point algorithm framework based on an adequate quadratic approximation of one convex function in the objective function, in a way reminiscent of Quasi-Newton methods. Utilizing the non-expansion property of the proximity operator we further investigate the global convergence of the proposed algorithm. Numerical experiments on image deblurring problem demonstrate that the proposed algorithm is very competitive with the current state-of-the-art algorithms in terms of computational efficiency.

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Authors and Affiliations

  1. Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing, 400038, Chongqing, People’s Republic of China

    Dai-Qiang Chen, Yan Zhou & Li-Juan Song

  2. School of Automation, Chongqing University, Changsha, Chongqing, 401331, Chongqing, People’s Republic of China

    Yan Zhou

Authors
  1. Dai-Qiang Chen
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  2. Yan Zhou
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  3. Li-Juan Song
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Correspondence to Dai-Qiang Chen.

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Communicated by: Helmut Pottmann.

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Chen, DQ., Zhou, Y. & Song, LJ. Fixed point algorithm based on adapted metric method for convex minimization problem with application to image deblurring. Adv Comput Math 42, 1287–1310 (2016). https://doi.org/10.1007/s10444-016-9462-3

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  • DOI: https://doi.org/10.1007/s10444-016-9462-3

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