A Study Of Image Denoising And Enhancement Based On Variation Method

With the development of science and technology,images as an important medium have become a necessary source of information.Images are inevitably affected by some factors during imaging,transmission,and storage.This often results in images with low contrast and noise pollution.In order to obtain clear and complete images,image denoising and enhancement have become important research issues in the field of computer vision and image processing.The variational method and partial differential equation method have mature mathematical theory basis and numerical calculation methods,and are widely applied to various fields of image processing.Therefore,this paper mainly studies some topics of variational methods and partial differential equations in image denoising and enhancement problem.In actual work,we may encounter such an image,its contrast needs to be improved and there is noise pollution.For this kind of problem,the traditional processing method has two choices: first enhance the contrast after denoising,or denoise after enhancing the contrast first.However,these two methods are not ideal for processing.Therefore,this paper first proposes a new model,coupled the L~p-norm-based denoising term and the contrast enhancement term.It combines the denoising process and the enhancement process of the image to simultaneously process the image with low contrast and noise pollution,to remove the noise,and enhance the image.The detailed information and low contrast improve the visual effect of the entire image.Secondly,this paper analyzes the theory of the model solution,mainly the existence and uniqueness of the model solution.The existence and uniqueness of the model solution are attributed to the existence and uniqueness of the corresponding evolution equation.The existence and uniqueness of the solution of the evolution equation are proved by the nonlinear semigroup theory of Hilbert space.Finally,the finite difference method is used in this paper to numerically discretize the model.However,the difference method is limited by the time step and is computationally time-consuming.Therefore,the fast Fourier transform acceleration algorithm is considered,and the longest time step in the algorithm is converted into the sum of several convolution operations,reducing the complexity of the entire calculation process and increasing the computer operating speed.The overall computational complexity of the algorithm is O(Nlog N),where N is the number of pixels of the input image.The experimental results of the model are compared with the experimental results of the different processing method to verify the ability of the model to remove noise at the same time.