将偏微分方程与能量泛函关联，用于彩色图像去噪
On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising
- 通过张量构造满足欧拉-拉格朗日方程的能量泛函
- 在彩色图像去噪任务中性能优于当前主流方法
- 适用于需要保真与平滑平衡的图像处理场景
研究了当偏微分方程（PDE）可视为由数据项和光滑项组成的能量泛函的欧拉-拉格朗日（E-L）方程的情形。给出了PDE作为对应泛函的E-L方程的必要条件。该能量泛函被应用于彩色图像去噪问题，实验表明其性能优于当前最先进的彩色图像去噪技术。
原文摘要 · Abstract (English)
The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques.
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