A Class Of Coupled Partial Differential Equations And Their Applications In Image Processing

In the process of image acquisition and processing,it is inevitable to be polluted by the outside world.The edge and details of the image are often obliterated,which seriously affects the acquisition of image information.Therefore,the image denoising is extremely important.In recent years,experts and scholars at home and abroad in the field of image processing have focused on image processing based on PDE method,which has attracted wide attention.The traditional PDE method uses the geometric structure features of the image to guide the nonlinear diffusion process.Because the image gradient is sensitive to the anomaly of high frequency noise,it will seriously affect the acquisition of the geometric structure features of the image.Therefore,the nonlinear diffusion process can not be effectively guided.Therefore,it is necessary to pre-filter the noisy image with Gaussian.However,after the Gaussian is smooth,the edge of the image becomes blurred to a certain extent,and the texture information is destroyed.Problems caused by image gradient sensitivity to noise,a new diffusion idea is proposed in this paper.The core of this method is to use the physical properties of the image instead of the geometric properties of the image.Specifically,the percolation field is established in the background of interferogram.The image is regarded as the porous medium material,the gray value of the image is taken as the permeability of the porous medium and the velocity in the percolation field is replaced by the gradient in the image to guide the diffusion process.This method preserves the advantages of the classical PDE method and avoids the Gaussian preprocessing of the image before filtering.The Darcy seepage equation is coupled with the nonlinear diffusion equation and a new multi-physical field coupling model(MPM)is established.MPM is a kind of PDE initial-boundary value problem,which has a clear physical background.In this paper,we first study the well-posed problem of MPM solution.In Hilbert space,we prove the existence and uniqueness of MPM solution in the sense of weak solution.Secondly,P-M model is a classical image processing model,and the "diffusion coefficient" in the diffusion process depends on the geometric structure of the image-gradient mode value.Because of the influence of noise,it is difficult to estimate the local characteristics ofthe image accurately.Gaussian prefiltering is usually used to preprocess the image.In order to avoid the problems caused by gradient and Gaussian prefiltering,the diffusion function is constructed by using the local physical properties of the image and the characteristics of the diffusion function are analyzed.Finally,the finite element simulation software COMSOL Multiphysical platform is used for numerical simulation.The experimental results show that the diffusion function has better edge preserving ability and faster convergence speed.When PSNR and EPI are equivalent to P-M,the time used is greatly shortened,the noise removal and image details and edge information can be better maintained.The model is an adaptive diffusion process and avoids the prior estimation before filtering.