Study On The PDE Method Of Image Restoration

In the real life,images are easily disturbed,distorted,and blurred by various factors.The quality of images is reduced,and the need for high quality images is essential in many fields.Therefore,image restoration is a very important link in image preprocessing.This paper mainly uses the theory of partial differential equation to restore the denoised image,and focuses on the improvement of the second-order and fourth-order partial differential equation for image denoising,which includes the following aspects:(1)Through the analysis of the advantages and disadvantages of the diffusion function in the second-order partial differential equation model,a new diffusion function is constructed,and it is more superior to the P-M model's diffusion function.Secondly,according to the inconvenience of existing models in selecting threshold,a new threshold function with adaptive ability is designed,Finally,a new diffusion model is proposed by combining the new diffusion function with the threshold function.The numerical experiments show that the model has the advantage of effectively removing noise and preserving edges,and preserving more details.(2)For the defect of "staircase effect" and "speckle effect",which produced by the second-order isotropic diffusion model and the fourth-order anisotropic diffusion.In this paper,an improved hybrid model based on anisotropic diffusion is proposed.In the flat area,the secnod-order anisotropic diffusion is used to denoise the image;and the fourth-order anisotropic diffusion is used to restore the image near the edge.The numerical experiments show that the improved model can effectively remove the noise,retain the edge,and retain more details of the image,reduce the computation and improve the peak signal to noise ratio and structural similarity of restored images.(3)Through the analysis of the advantages and disadvantages of the mixed model of the second-order and fourth-order partial differential equations,this paper introduces the difference curvature operator to construct the new weight parameters,and then combines the TV model and the Y-K model,and establishes a new adaptive image restoration model.The numerical experiment results show that the new model effectively removes the noise and preserves the edge,while preserving more details,and simplifies the process of image processing,reduces the amount of calculation and improves the quality of the image.