Research And Application Of Edge-Preserving Denoising Algorithm Based On Anisotropic Diffusion

In the image denoising field,the anisotropic diffusion method based on the Partial Differential Equation has been a hot spot of research,the methods can preserve the edges while denoising because of the weak diffusion characteristics of diffusion equation in edge direction of image and are recognized by researchers.In constant research,the distrubution of the energy radio between effective signal and noise is nonuniform in the full frequency band,so that the traditional full-band denoising methiods have the problem that the edge information is smoothed due to excessive denoising.Therefore,in this paper,we mainly based on the anisotropic diffusion method and the thought of frequency division,combined with the novel variational mode decomposition method,by using the gradient value and frequency of the data to overcoming the difficult of selecting the threshold in the chambolle and lions' s alternative model(CL method).Thus,a new dynamic threshold operator is established,and a new dynamic anisotropic diffusion method based on frequency division is proposed and applied to the seismic data denoising.The main contents and achievements of this paper are as follows:(1)Introducing the novel signal decomposition methods.Four commonly used decomposition methods for non-linear and non-stationary signals are systematically introduced in this paper: Empirical Mode Decomposition,Ensemble Empirical Mode Decomposition,Complete Ensemble Empirical Mode Decomposition and Variational Modal Decomposition.In order to compare the accuracy of signal component decomposition and anti-noise ability of these four methods,according to the characteristics of seismic signals(typical non-linear non-stationary signals)and the purpose of edge-preserving denoising,a multi-component seismic signal and a local noise-added signal are established,and then apply these four methods to these two synthetic signals,respectively.According to the decomposition results of time domain and frequency domain,we can see that the Variational Modal Decomposition method not only has a solid mathematical theoretical foundation,but also has the best anti-mode aliasing ability and anti-noise ability.It is very suitable for the thought of frequency division denoising in the following part of this paper.(2)The traditional methods based on anisotropic diffusion method are introduced.Anisotropic diffusion method is a nonlinear denoising method based on Partial Differential Equation.It uses directional diffusion equation instead of Gaussian smoothing filter to achieve the purpose of protecting the information of edges while denoising.In this paper,we have mainly introduced three traditional anisotropic diffusion filtering methods: P&M,Total Variation method(TV method)and CL method.The advantages and disadvantages of each method are obtained on the basis of the theory of the methods,then the anisotropic diffusion method based on adaptive threshold is introduced.According to the results of model and field data,they are verified that the anisotropic diffusion method based on adaptive threshold has faster computing efficiency.Besides,comparing to the TV method and CL method,the anisotropic diffusion method based on adaptive threshold has the best performance in edge preserving while denoising.(3)In this paper,we have proposed an adaptive hybrid diffusion model using variational mode decomposition(VMD).Firstly,we have introduced the theories of the signal decomposition methods and comprised the results obtained by those method.According to the results,we choose the VMD as the decomposition method of our method.Then,combining the dynamic threshold based on frequency,proposed the new edge-preserving denoising method named an adaptive hybrid diffusion model.We firstly apply the VMD to the data and obtained the Intrinsic Mode Function(IMF)section which are in the different frequency domain.After decomposition,the proposed dynamic threshold according to the pixel gradient value of each IMF section to be calculated adaptively,and the threshold divides each IMF section into different areas,which stands for noise or structures respectively.Then,the appropriate filtering method is chosen to attenuate noise.Finally,the denoised result of the seismic data is obtained by superposition the denoised IMF sections.(4)We applied the proposed method named a dynamic threshold method based on anisotropic diffusion into model data and field data and compared with other edge-preserving denoising methods.According to the results,the proposed method can effectively suppress the random noise and improve the signal-to-noise ratio of the data while keeping the characteristic information of the original seismic data as much as possible.In addition,the weak amplitude is strengthened in the process of restoration,and the contact relation of underground layer is more obvious which improves the lateral resolution of the data.