PDE-based deconvolution with forward-backward diffusivities and diffusion tensors

  • Authors:

  • Martin Welk;David Theis;Thomas Brox;Joachim Weickert

  • Affiliations:

  • Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany

  • Venue:
  • Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
  • Year:
  • 2005

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Abstract

Deblurring with a spatially invariant kernel of arbitrary shape is a frequent problem in image processing. We address this task by studying nonconvex variational functionals that lead to diffusion-reaction equations of Perona–Malik type. Further we consider novel deblurring PDEs with anisotropic diffusion tensors. In order to improve deblurring quality we propose a continuation strategy in which the diffusion weight is reduced during the process. To evaluate our methods, we compare them to two established techniques: Wiener filtering which is regarded as the best linear filter, and a total variation based deconvolution which is the most widespread deblurring PDE. The experiments confirm the favourable performance of our methods, both visually and in terms of signal-to-noise ratio.