Research On Image Denoising Algorithm Based On Partial Differential Equation And Recursive Filter

With the continuous development of electronic technology and the popularization of information technology in today's society,digital images have been widely used in production and life,biomedicine,military remote sensing and other fields.This also makes image denoising technology a very popular research project with great scientific research value and application prospects.In the study of image denoising,how to remove the noise while taking into account the texture details and edge features of the image is a challenging and important problem.An image denoising method based on partial differential equations can build a continuous mathematical model representing an image according to the characteristics of the image,so that the image evolves following a specific partial differential equation,and the result of image denoising can be obtained by solving the equation.This paper mainly studies the total variation method and anisotropic diffusion method in the partial differential equation method of image processing,analyzes the denoising principle of its classic model to improve the deficiencies of the model,and combines new algorithms to construct new Denoising model.Finally,simulation experiments and data analysis are used to prove the advantages of the new model.The specific research process is as follows:1.The method of total variation denoising for image processing is studied.By analyzing the problem of "staircase effect" in ROF model,an improved method of high order total variation is proposed.Aiming at the lack of edge protection ability of high-order total variational denoising model,a weighted adaptive total variational denoising model is proposed.The experimental results show that compared with the traditional denoising model,the new model can effectively suppress the staircase effect in the denoising process,while protecting the texture details in the edge area of the image.2.This paper studies the theory of anisotropic diffusion method for image denoising,analyzes the advantages of PM model and its defects such as "morbid state",and proposes(1)an improved PM diffusion model,protecting the edge structural features of the image by splitting and controlling of the diffusion direction;(2)a recursive anisotropic diffusion model,using a recursive filtering algorithm to reduce the number of iterations in the denoisingprocess,thereby retaining the image's texture details;(3)An image denoising model combining improved PM and recursive filtering,being able to take into account the texture details and edge features of the image while removing noise.Experimental results show that the new model is superior to traditional denoising models in terms of denoising performance and texture structure protection.