提出新型张量变分模型GETV，提升图像去噪效果
A Tensor Variational Formulation of Gradient Energy Total Variation
- 引入梯度能量张量构建新变分模型
- 理论证明GETV为凸函数，确保解唯一
- 在灰度与彩色图像上优于主流去噪方法
本文提出一种基于张量的总变差新变分方法——梯度能量总变差（GETV）。通过引入梯度能量张量，得到对应的欧拉-拉格朗日（E-L）方程为张量型总变差偏微分方程。进一步证明GETV是凸泛函。该方法相较于常用的结构张量，可实现对应E-L方程的严格推导。实验结果表明，GETV在灰度和彩色图像去噪任务中表现优于扩展各向异性扩散（EAD）和总变差（TV）等先进变分方法。
原文摘要 · Abstract (English)
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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