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A Tensor Variational Formulation of Gradient Energy Total Variation

  • Freddie Åström
  • George Baravdish
  • Michael Felsberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)

Abstract

We present a novel variational approach to a tensor-based total variation formulation which is called gradient energy total variation, GETV. We introduce the gradient energy tensor [6] into the GETV and show that the corresponding Euler-Lagrange (E-L) equation is a tensor-based partial differential equation of total variation type. Furthermore, we give a proof which shows that GETV is a convex functional. This approach, in contrast to the commonly used structure tensor, enables a formal derivation of the corresponding E-L equation. Experimental results suggest that GETV compares favourably to other state of the art variational denoising methods such as extended anisotropic diffusion (EAD)[1] and total variation (TV) [18] for gray-scale and colour images.

Keywords

Image Structure Regularization Term Structure Tensor Orthonormal Eigenvector Anisotropic Total Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Freddie Åström
    • 1
    • 2
  • George Baravdish
    • 3
  • Michael Felsberg
    • 1
  1. 1.Computer Vision LaboratoryLinköping UniversitySweden
  2. 2.Center for Medical Image Science and Visualization (CMIV)Linköping UniversitySweden
  3. 3.Department of Science and TechnologyLinköping UniversitySweden

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