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  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
, 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
(TV)  for gray-scale and colour images.