Study Of Image Denoising And Decomposition Model And Its Algorithm Based On TV And The Fractional Order Derivatives

Images are the most visual form in the process of information transmission.However images will be damaged by noise,which affects the quality and makes it difficult for people to analyze the images.The noise in the observed images should be removed before we use them.Image denoising aims to restore the original clean image from the noised image and give people a better visual effect.There are different types of noise in the noisy image,and the additive noise is the most widely studied.We mainly focus on additive noise in this paper.In addition,image decomposition is also an important research topic in the field of image processing.Image decomposition is widely used and the quality of image decomposition has a direct impact on the quality of subsequent problems in image processing.The main ideas of this paper are as follows:1)TV model has always been a classical model in the fields of image processing but it will produce staircase effect near image edges.To get better denoising effect,the fractional derivatives with order less than 1 is introduced to describe the noise part of the image.The fractional derivatives can remove noise adaptively.2)Some texture information is mistakenly removed as noise in TV model,which makes the effect of image decomposition unsatisfactory.As is well known,an image contains many different parts and different parts can be modeled by different methods according to their own characters.Based on this idea,the texture part is described by the fractional order with order greater than 1.The fractional derivatives can not only enhance the edge detail of the image,but also retain more texture details.3)Based on the above research,the cartoon part is depicted by the total variational norm while the noise and texture are modeled by different fractional derivatives.Then a new fractional variational model is proposed which combines the total variational minimization and the fractional order derivatives.Finally we solve the new model by the alternate minimization method and Euler-Lagrange equation method and numerical experiments are carried out with MATLAB.The new model can not only remove the noise and suppress the staircase effect but also have some advantages in texture preservation.4)In this paper,the new model is compared with the other available image denoising and decomposing models.From the comparison of signal to noise ratio and peak signal to noise ratio,we can know that the new model is a kind of practical image denoising and decomposition model.It has some advantages in removing noise and preserving texture.