能量泛函及Euler-Lagrange方程在图像降噪中的应用研究  

Research on the Application of Energy Functional and Euler-Lagrange Equation in Image Denoising

作　　者：王海燕[1] WANG Haiyan(Luoding Polytechnic,Luoding Guangdong 527200,China)

机构地区：[1]罗定职业技术学院,广东罗定527200

出　　处：《佳木斯大学学报（自然科学版）》2024年第6期173-175,180,共4页Journal of Jiamusi University：Natural Science Edition

摘　　要：研究了自适应分数阶偏微分方程修正模型的能量泛函及Euler-Lagrange方程。首先,定义了自适应分数阶偏微分方程修正模型的能量泛函,其中包含未知函数和拉格朗日乘子的集合。然后,通过求解能量泛函的极值方程,推导出了Euler-Lagrange方程。最后,讨论了Euler-Lagrange方程在自适应分数阶偏微分方程修正模型中的应用。This paper investigates the energy functional and Euler-Lagrange equations of adaptive fractional partial differential equation correction models.Initially,we define the energy functional of the adaptive fractional partial differential equation correction model,comprising a set of unknown functions and Lagrange multipliers.Subsequently,by solving the extremal equation of the energy functional,we derive the Euler-Lagrange equations.Finally,we discuss the application of the Euler-Lagrange equations within the context of adaptive fractional partial differential equation correction models.

关 键 词：分数阶微分方程 能量泛函 EULER-LAGRANGE方程 修正模型 

分 类 号：O241.82[理学—计算数学]