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arXiv · 2608.29172

A Tensor Variational Formulation of Gradient Energy Total Variation

Freddie Åström·George Baravdish·Michael Felsberg
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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.

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Freddie Åström, George Baravdish, Michael Felsberg. 2026-08-29. A Tensor Variational Formulation of Gradient Energy Total Variation. https://doi.org/10.1007/978-3-319-14612-6_23

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