Introducing diffusion tensor to high order variational model for image reconstruction

Jinming Duan, Wil O.C. Ward, Luke Sibbett, Zhenkuan Pan*, Li Bai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler's elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

Original languageEnglish
Pages (from-to)323-336
Number of pages14
JournalDigital Signal Processing
Early online date12 Jul 2017
Publication statusPublished - 1 Oct 2017


  • ADMM
  • Diffusion tensor
  • Fast Fourier transform
  • Frobenius norm
  • Hessian
  • Total variation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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