A Tensor Variational Formulation of Gradient Energy Total Variation
Computer Vision and Pattern Recognition
Summary
The authors introduce a new way to reduce noise in images called gradient energy total variation (GETV), which uses a special kind of math object called a tensor to analyze image details. They show that GETV leads to a certain equation that helps improve image smoothing and prove that their method is mathematically stable (convex). Unlike older methods that use a structure tensor, their approach allows for a clearer derivation of the key equation. Tests show that GETV works well compared to other popular image denoising techniques on both black-and-white and color images.
Authors
Freddie Åström, George Baravdish, Michael Felsberg
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.