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PDE based deconvolution with forward-backward diffusivities and diffusion tensors

M. Welk, D. Theis, Thomas Brox, J. Weickert
Scale Space and PDE Methods in Computer Vision, Springer, LNCS: 585-597, Apr. 2005
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.


Other associated files : welk_ss05.pdf [315KB]  

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BibTex reference

@InProceedings{Bro05c,
  author       = "M. Welk and D. Theis and T. Brox and J. Weickert",
  title        = "PDE based deconvolution with forward-backward diffusivities and diffusion tensors",
  booktitle    = "Scale Space and PDE Methods in Computer Vision",
  series       = "Lecture Notes in Computer Science",
  pages        = "585-597",
  month        = "Apr.",
  year         = "2005",
  publisher    = "Springer",
  url          = "http://lmb.informatik.uni-freiburg.de/Publications/2005/Bro05c"
}

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