Image Denoising And Enhanced Based On Fractional Calculus Method Research

In recent years,image processing methods based on fractional calculus have attracted attention due to the finer detail of capturing image details and have become a hot research field.However,unlike the partial-order partial differential equation image processing method,the effect of edge and texture detail is not ideal enough in image processing based on fractional calculus theory.In general,there are not many image processing methods based on fractional calculus,and the effectiveness needs to be further improved.In this paper,we study the fractional calculus method of image enhancement and image denoising,based on the theory of fractional calculus,The Caputo fractional differential mask operator and a fractional hybrid denoising method are studied respectively.The main innovations are as follows:1.A Caputo fractional differential mask operator with order(1,2)is proposed,and its general order is generalized.And the general order situation is promoted.Firstly,the characteristics of Caputo differential expression and its mask operator in Grünwald-Letnikov,Riemann-Liouville and order intervals in the range of(0,1)are analyzed,on the basis of this,the forward differential approximation method is used to construct the Caputo fractional differential mask operator of(1,2)interval range,and the approximation error of the difference expression is analyzed and proved;Furthermore,the constructed Caputo fractional differential mask operator of the(1,2)interval range is extended to the general(m-1,m)(m>2)order range,and the general expression is given;Finally,the constructed Caputo fractional differential mask operator is applied to image enhancement,compared to the fractional differential mask operators of Grünwald-Letnikov and Riemann-Liouville,the experimental results show that the Caputo fractional differential mask operator of the(1,2)interval range constructed in this paper can effectively maintain and enhance the edge texture information of the image.2.A fractional-order hybrid model based on image denoising in Fourier transform domain is proposed.In-depth study and analysis of the fractional-order TV model can enhance the edge information well in the process of denoising,the fractional-order PM model maintains texture detail information while effectively removing noise.Then,using a monotonically increasing weight function with a range of values and an independent variable of the image gradient,the respective advantages of the fractional-order TV denoising model and the fractional-order PM denoising model are combined.An image denoising fractional-order hybrid model based on adaptive weight function of image gradient values is proposed,and the order of the model is determined by the gradient and variance of the noisy image,further research on the numerical calculation method of the model is carried out.The simulation results show that the fractional-order hybrid denoising model proposed in this paper can effectively remove the edge and texture details of the image while effectively removing noise.