The Usability Analysis Of Several Image Denoising Methods Based On PDEs

Image is one of the world's most important means of objective understanding,particular,with the rapid Development multi-media technology,image becomes more closely with human life.At the same time,the rapid development of computer science,as well as the spread of digital images and image display devices,have provided good conditions for the development of image processing,and have become a major driving force for its development.In all types of imaging systems,as a result of image transmission and conversion,such as imaging,copy,scan,transmit,display,the original image has to be incorporated with noise inevitable.The edge of images,information and other important details of images often immersed in noise signals,which brings a great impact to the follow-up of image Processing such as edge detection, image segmentation,and image matching. Therefore, it is necessary to do image denoising in the pre-processing stage.Image denoising is the a kind technical widely used in image pre-processing applications field, its principle is the use of the distribution difference of noise signals and image signals in the frequency domain. Image signal is mainly distributed in the low-frequency region. The noise pixels locate in high-frequency region because of the poor correlation with and the surroundingpixels. Traditional space or frequency domain denoising method is based on or generally similar with a low-pass filter, filtering out the high frequency signal components to achieve denoising. However, some mutations image information (such as the edge features) are also in the high frequency image signal region, and these mutations have more impact to visual images than common image signal informations . How to filter image noise and better maintain the the texture details of image have become the central issue of image denoising area.The existing image denoising methods can be roughly classified as four types: methods Based on the frequency domain, methods Based on the space domain, methods based on Bayesian statistical theory and methods based on machine learning .However,in the mean time of filtering noise using these conventional methods,we often lose the high-frequency information of the image,and cause by the fuzzy of edge and texture. So, in the process of denoising,there is a conflict between noise suppression and he reservation of edge (no loss of spatial resolution),and we need to find better methods of denoising, which can not only suppress noise ,but also maintain the edge and texture information, in order to better rehabilitate the degradation of image quality caused by noise pollution.In recent years,image processing method denoising based on PDEs has been widely recognized in the field of image.This is because in the mean time of smoothing noise,this method also can make the details of images,such as the edge and Texture protected. The basic idea of image denoising method based on PDEs ,which is originated from the constrained optimization ,energy minimization methods and variational methods ,is reducing the issue to a minimal functional problem, and then applying variational methods to export one or a group of Partial differential equations, finally,solving these equations using numerical method and get the wanted numerical solution. In face,this numerical solution is a restored image.For image denoising problems, this paper introduces the background of image denoising, and the general image denoising Method is generally broad. Then, bringing in image processing method based on PDEs which has got extensive attention.In the second chapter of this paper, we introduce the P-M model based on and its improved algorithm. The improved algorithm selects the following form of spread function in the original P-M model framework:elseExperiments show that after selecting spread function as defined above, the improved P-M method not only improves the speed of smoothing, but also reaches a better smoothing effect.Meanwhile this improved method avoids negative issues such as fuzzy boundaries caused by a number of iterative, and has better practicability and feasibility.In the third chapter of this paper, a more detailed description is given to the construction method of TV denoising model, and we list two improving methods of the TV denoising model : Generalized TV denoising model and the Adaptive TV denoising model.Adaptive TV denoising model is as follows: The Adaptive TV denoising model:andp(x,y)=(?),G_σis Gaussian filter, andσ> 0.Experiments show that adaptived TV denoising model overcomes the ladder effect introduced by TV model, and determines the adaptive program by the use of gradient information of each image pixel, which lead to both the removal of noise and the maintenance of details of image.In the forth chapter of this paper, we introduce a typical fourth-order partial differential equations denoising model: You-Kaveh high-order denois- ing model and its improved algorithm.The experiments show that this improved algorithm, while in the denoising, Well maintained the detail informations and the edge of the image , and has better practicality.