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This article comprehensively and systematically expounds the development trends and basic theory of partial differential methods, analyzes the characteristics of sampling multiscale transformation in detail, and deeply studies the network image denoising and network image restoration methods that perform partial differential diffusion in the pixel domain and the transform domain. An adaptive diffusion method of partial differential equations is proposed. Among them, the key parameters can be adaptively changed according to the curvature and gradient of the local geometric information of the network image, and the diffusion direction and intensity of the diffusion can be controlled. First, using the principle of variation, we derive the Euler equation corresponding to the diffusion method of partial differential equations and analyze its diffusion ability using the local orthogonal coordinate system of the network image. Based on the theoretical analysis of public opinion, this article applies opinion mining technology to the online public opinion early warning system to achieve the purpose of grasping the opinions of netizens in time and guiding the trend of public opinion. Opinion mining is the use of natural language processing technology to automatically extract the emotional tendencies and evaluation objects contained in the subjective text. In the edge area of the network image, the diffusion along the edge direction should have a large diffusion coefficient, and the diffusion along the vertical edge direction should have a small diffusion coefficient; in the flat area of the network image, it diffuses to the surrounding with equal intensity, and the diffusion intensity value is relatively high. Secondly, based on the analysis of the adaptive partial differential equation diffusion method, using the half-point difference format, a numerical method for network image recognition is designed. Both theoretical analysis and experimental results show that the network image recognition model based on adaptive partial differential equation diffusion is more effective than the model based on partial differential equation recognition; at the same time, experiments show that the network image recognition model based on adaptive partial differential equation diffusion is more effective than the network image recognition model based on ordinary diffusion. The network image recognition model based on constant partial differential equation diffusion is more effective in improving the quality of network image recognition.

Analysis and Recognition Method of Internet Image Public Opinion Based on Partial Differential Equation