自适应分数阶偏微分方程修正模型的能量泛函及Euler-Lagrange方程研究  

Adaptive Fractional Order Partial Differential Equation Correction Model for Energy Flooding and Euler-Lagrange Equation Study

作　　者：王晓霞[1] WANG Xiaoxia(College of Science,Qiqihar University,Qiqihar Heilongjiang 161006,China)

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《佳木斯大学学报（自然科学版）》2024年第9期172-176,共5页Journal of Jiamusi University：Natural Science Edition

摘　　要：首先对分数阶微分方程进行构建,结合全变分项,提出了修正的自适应分数阶偏微分方程模型。研究首先确定出分数阶偏分去噪模型的最优分数阶数,当分数阶次为1.8时,峰值信噪比和结构相似度达到33.12和0.874,均方根误差降低至5.62。然后将研究提出的模型与全变分模型、分数阶偏分去噪模型等在图像上进行对比实验,研究提出的模型在峰值信噪比、结构相似度上达到最高,分别为29.045与0.839,均方根误差为9.427,表明模型能够抑制阶梯效应,具有优越的去噪性能。The study firstly constructs the fractional order differential equation and combines the full variational term to propose the modified adaptive fractional order partial differential equation model.The study first determines the optimal fractional order for the fractional order partial denoising model,and at a fractional order of 1.8,the peak signal-to-noise ratio and structural similarity reach 33.12 and 0.874,and the root-mean-square error is reduced to 5.62.Then the proposed model is compared with the full variational model and the fractional order partial denoising model in theimage for comparison experiments,and the proposed model achieves the highest peak signal-to-noise ratio and structural similarity reaches the highest,29.045 and 0.839 respectively,and the root mean square error is 9.427,which indicates that the model is able to suppress the step effect and has superior denoising performance.

关 键 词：自适应 分数阶 能量泛函 均方根误差 偏微分方程 

分 类 号：TP751.1[自动化与计算机技术—检测技术与自动化装置]