Research On Image Denoising Algorithms Based On Partial Differential Equation And Multi-Directional Weighted Mean Filter

Most of image denoising methods blur edges after denoising to a certain extent.Therefore,it is desirable for deeply researching image processing method to establish an image denoising algorithm which can not only remove noise but also preserve edges.For the common Gaussian noise,salt-and-pepper noise and the mixture of Gaussian noise and salt-and-pepper noise,this thesis proposes the corresponding image denoising algorithms based on the partial differential equation diffusion model and multi-directional weighted mean filter.In the first part,an adaptive anisotropic diffusion(AAD)model based on image feature enhancement is established to overcome the drawback of the coherence-enhancing anisotropic diffusion model,which often induces false edges in the smooth regions and cannot preserve details well.The AAD model firstly analyzes the image features and introduces an image feature classification method to finely classify image features as smooth regions,edges,corners and isolated noises.Secondly,according to the classification result,the eigenvalues of diffusion tensor are designed to conduct the diffusion rate in different direction of different feature.Finally,the proposed model can achieve the adaptive diffusion.Experimental results show that the AAD model can not only effectively remove the Gaussian noise but also preserve edges and corners.In the second part,a multi-directional weighted mean(MWM)filter based on two-stage restoration scheme is proposed to remove salt-and-pepper noise in the case of different noise density,which divides the filtering process into two phases as noise detection and noise restoration.In the noise detection phase,the MWM filter firstly introduces a characteristic difference parameter to judge the difference between different pixels,and combines the characteristic difference parameter and gray level extreme to detect noise corrupted pixels.In the noise restoration phase,a two-stage restoration scheme is introduced to restore the gray levels of noise corrupted pixels twice as the primary noise restoration and second noise restoration.Besides,a multi-directional weighted mean filter is posed to secondly restore the gray levels of noise corrupted pixels in the second restoration scheme.Experimental results show that the MWM filter has a strong ability in terms of image denoising and edge preservation.In the third part,in order to further improve the quality of the denoised image,an adaptive multi-directional weighted mean(AMWM)filter is established based on the MWM filter.In order to improve the accuracy of noise detection,a variance parameter is introduced to judge the difference between different pixels.And a noise detector which combines the variance parameter and gray level extreme is designed to detect noise corrupted pixels.After noise detection,an adaptive multi-directional weighted mean filter is posed to secondly restore the gray levels of noise corrupted pixels,which can adaptively select the size of restoration window.Experimental results show that the AMWM filter can perform better than MWM filter and other compared filters in terms of noise suppression and edge preservation.In the fourth part,a mixed noise(MN)filter combining multi-directional weighted mean filter and adaptive anisotropic diffusion model is proposed to remove the mixture of Gaussian noise and salt-and-pepper noise.The MN filter firstly introduces a noise classification method to divide all noise corrupted pixels into two types,including the pixels corrupted by salt-andpepper noise and the pixels corrupted by Gaussian noise.Secondly,the gray levels of pixels corrupted by salt-and-pepper noise are restored by the multi-directional weighted mean filter.Finally,the pixels corrupted by Gaussian noise in the initial denoised image are restored by the adaptive anisotropic diffusion model.Experimental results show that the MN filter can not only effectively remove the mixed noise but also preserve edges and details.The proposed image denoising algorithms can obtain a good balance between image denoising and edge preservation,which can effectively remove noise meanwhile preserve edges and details.