Implementation of high-order variational models made easy for image processing

Wenqi Lu, Jinming Duan, Zhaowen Qiu*, Zhenkuan Pan, Ryan Wen Liu, Li Bai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)


High-order variational models are powerful methods for image processing and analysis, but they can lead to complicated high-order nonlinear partial differential equations that are difficult to discretise to solve computationally. In this paper, we present some representative high-order variational models and provide detailed descretisation of these models and numerical implementation of the split Bregman algorithm for solving these models using the fast Fourier transform. We demonstrate the advantages and disadvantages of these high-order models in the context of image denoising through extensive experiments. The methods and techniques can also be used for other applications, such as image decomposition, inpainting and segmentation.

Original languageEnglish
Pages (from-to)4208-4233
Number of pages26
JournalMathematical Methods in the Applied Sciences
Issue number14
Early online date7 Mar 2016
Publication statusPublished - 30 Sept 2016


  • bounded Hessian
  • image processing
  • split Bregman algorithm
  • total curvature
  • total generalised variation
  • total variation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)


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