A fixed-point algorithm for second-order total variation models in image denoising

  • Tianling Gao
  • Xiaofei Wang
  • Qiang LiuEmail author
  • Zhiguang Zhang


In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix. The algorithms are tested on various images to verify our proposed convergence conditions. The experiments compared with the split Bregman algorithms demonstrate that fixed-point algorithms could solve the second-order functional minimization problem stably and effectively.


Fixed-point algorithm Convergence High-order total variation Image denoising 

Mathematics Subject Classification

68U10 65K10 



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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsShenzhen UniversityShenzhenPeople’s Republic of China

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