A Tensor Variational Formulation of Gradient Energy Total Variation

2026-08-29

AI Summary

本文提出了一种基于张量的梯度能量总变差（GETV）方法，通过引入梯度能量张量来解决图像去噪问题，并证明了其为凸泛函。

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.

Problem

• Gradient Energy Total Variation
• Image Denoising
• Variational Approach

Innovation

• Gradient Energy Tensor
• Total Variation
• Euler-Lagrange Equation
• Convex Functional