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Published in:
2015 | OriginalPaper | Chapter
A Tensor Variational Formulation of Gradient Energy Total Variation
Authors : Freddie Åström, George Baravdish, Michael Felsberg
Published in: Energy Minimization Methods in Computer Vision and Pattern Recognition
Publisher: Springer International Publishing
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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.