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 tensorbased 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.
CITATION STYLE
Åström, F., Baravdish, G., & Felsberg, M. (2015). A tensor variational formulation of gradient energy total variation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8932, pp. 307–320). Springer Verlag. https://doi.org/10.1007/978-3-319-14612-6_23
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