Research On Image Denoising And Enhancement Based On Adaptive Order Of Fractional Partial Differential Equations

Recently,the method based on fractional order partial differential equation has been used in image processing.In the process of image processing,the traditional value of the fractional order is often chosen by the experience or a large number of experiments,it can't realize the adaptation,and it does not give full play to the excellent characteristics of the fractional differential.In this thesis,we mainly research on the algorithms for image denoising and enhancement based on adaptive order of fractional partial differential equations.The main work and conclusions of this thesis are as follows:1.An image denoising algorithm based on adaptive fractional order anisotropic diffusion is proposed.In the proposed model,the complexity of the local image texture is reflected by the local variance,and the order of the fractional differentiation is determined adaptively.For calculating the fractional differentiation,we employ the discrete Fourier transform and the dynamic evolution process is computed in the frequency domain.Experimental results show that the peak signal-to-noise ratio and structural similarity index measurement of the proposed image denoising algorithm are better than that of other compared algorithms.The proposed algorithm not only can keep the detailed image information and edge information,but also obtain a good visual effect.2.The fractional calculus operator for image denoising is constructed based on the characteristic of local entropy and the gradient feature,and an adaptive fractional calculus image denoising algorithm is proposed.Firstly,the affect on the entropy and gradient by noise are analyzed respectively.Then by regarding the noise points as small probability events in an image,the noise points,edges,texture regions and smooth regions are divided combining with the local structure.Finally,for improving the image denoising effect,we consider employing different fractional orders to deal with different pixels and a piecewise function is constructed to make the differential order to be adaptive.The function is with respect to the local entropy and gradient on the pixel.The experimental results show that the peak signal to noise ratio and the entropy of the proposed adaptive fractional calculus image denoising algorithm are higher than that of the other compared algorithms.The proposed algorithm can not only preserve image edges and texture information while removing the noise,but also obtain a good visual effect.3.Combining with the local gradient,local information entropy and local variance,which relate to the image texture,an adaptive fractional differential image enhancement algorithm is proposed,and applied to some related medical images.Based on the information entropy and average gradient,which can be the quantitative assessment criteria for texture analysis,the enhanced image was analyzed and compared.Experimental results show that compared with other algorithms,adaptive fractional differential algorithm can not only enhance the image edge and texture,but also keep smooth regions of details and gain better visual effect.