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)


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.


Image Structure Regularization Term Structure Tensor Orthonormal Eigenvector Anisotropic Total Variation 
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© 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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