发表机构
Linköping University; Center for Medical Image Science and Visualization (CMIV); Department of Science and Technology, Linköping University（林雪平大学; 医学图像科学与可视化中心（CMIV）; 林雪平大学科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了梯度能量全变分（GETV）的张量变分形式，证明其为凸泛函，可形式推导欧拉-拉格朗日方程，实验显示其在图像去噪上优于EAD、TV等方法。
AI 中文摘要
我们提出了一种基于张量的全变分形式的新型变分方法，该形式称为梯度能量全变分（GETV）。我们将梯度能量张量[6]引入GETV，并证明对应的欧拉-拉格朗日（E-L）方程是一种基于张量的全变分型偏微分方程。此外，我们给出了证明，表明GETV是一个凸泛函。与常用的结构张量相比，该方法能够对对应的E-L方程进行形式推导。实验结果表明，对于灰度图像和彩色图像，GETV与其他最先进的变分去噪方法（如扩展各向异性扩散（EAD）[1]和全变分（TV）[18]）相比表现更优。
英文摘要
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.
Journal refEnergy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932, pp. 307-320, Springer, 2015
DOI：10.1007/978-3-319-14612-6_23
