Problem
Research questions and friction points this paper is trying to address.
partial differential equation
Euler-Lagrange equation
energy functional
color image denoising
On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising
🤖 AI Summary
研究了基于张量的偏微分方程及其对应的变分公式在彩色图像去噪中的应用，提出了一种与现有技术相比具有竞争力的方法。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Tensor-based PDEs
Variational Formulations
Color Image Denoising
Euler-Lagrange Equation
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