Research And Application Of Image Denoising Methods Based On Partial Differential Equation And Non-local Means

As an important transmitter of information,the image plays an irreplaceable role in human life.In recent years,with the growing maturity of computer vision theory,the image processing technology is widely applied in the fields of medical treatment,security and protection,agriculture,industry,transportation and other fields.However,the image will be interfered by many kinds of noise signals in the process of acquisition,transmission and storage.This will not only affect the visual effect of the image,but also affect the accuracy of subsequent pattern recognition and image understanding.At present,with the rapid development of artificial intelligence,the requirement for the image quality is becoming higher and higher.For example,in the field of microelectronic industry,the ball grid array(BGA)solder joint X-ray image with the clear edge contour and the high signal-to-noise ratio is a key prerequisite for accurately detecting the internal defects of solder joints.Therefore,in order to obtain the clean and clear denoised image,the research on image denoising methods with the high performance is of the great theoretical significance and application value.In view of this,this dissertation mainly focuses on the image denoising methods based on the partial differential equation and non-local means and their application in the BGA solder joint X-ray image.The main research contents are summarized as follows:1.On the basis of the research on the second-order anisotropic diffusion equation,two new anisotropic diffusion models were proposed for image denoising:(1)The traditional second-order anisotropic diffusion equation is easy to blur image details and cause staircase effect.For this reason,a new anisotropic diffusion equation based on the Sobel operators and the sparse representation theory was proposed for image denoising.Firstly,structure features of the image were extracted with four directional Sobel operators.Then,the variance of the absolute value of four directional feature values was used as a new edge detector to guide the extent of smoothing on image features.Meanwhile,the K-singular value decomposition(K-SVD)denoising model based on the sparse representation theory was applied to the diffusion process.In this K-SVD model,the representation error boundary was decreased with the increase of the iteration number.Finally,the optimal solution of the proposed model was solved by the addition operator splitting(AOS)scheme.Experimental results show that the proposed model can effectively smooth noise and avoid staircase effect while preserving important structure features of the image.(2)In order to relieve the contradiction between edge preservation and noise removal in the image denoising process,a new model combining the patch-similarity-based anisotropic diffusion and the shock filter was proposed for image denoising and enhancement.The proposed model made use of the patch-similarity-based anisotropic diffusion model to remove noise and simultaneously introduced the shock filter to enhance the important structure features in the image.Moreover,the function with respect to the modulus of the image gradient was constructed to adaptively adjust the enhancement coefficient in the homogenous region,the detail region and the edge region of the image.This function could suppress noise amplification and overshoot phenomenon when the proposed model enhanced image details.Two sets of experiments on standard gray images and BGA solder joint X-ray images were used to demonstrate the effectiveness of the proposed model.Experimental results show that the proposed model can preserve and enhance the important structure information of the image while removing noise.2.On the basis of the research on the fourth-order isotropic diffusion equation and anisotropic diffusion equation,two new fourth-order partial differential equations were proposed for image denoising:(1)The traditional fourth-order partial differential equation is extremely sensitive to noise and can not effectively preserve image details.For this reason,a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature was proposed for image denoising.Firstly,using the image patch similarity to take the place of the pixel similarity,a new edge detector called the patch similarity modulus was designed,which was strongly robust to noise.Then,the difference curvature and the patch similarity modulus were simultaneously used as the edge indicator in the diffusion function,which adjusted the size of the diffusion coefficient in the edge region and the flat region of the image.Experimental results show that the proposed model can effectively suppress speckle artifacts and has a better detail-preserving capability.(2)The fourth-order isotropic diffusion equation blurs image edges and the fourth-order anisotropic diffusion equation causes staircase artifacts.For this reason,an adaptive fourth-order partial differential equation based on the modulus of the image gradient was proposed for image denoising.Firstly,the modulus of the image gradient was introduced to construct the detection function of the image feature information.Then,according to the different features of the image,the diffusion coefficients in the normal direction and the tangent direction were adaptively adjusted by the feature detection function.In the flat and ramp regions,the proposed model acted as the isotropic diffusion equation to remove noise.In the edge region,the proposed model acted as the anisotropic diffusion equation to preserve image features.The standard gray images and BGA solder joint X-ray images were used to demonstrate the effectiveness of the proposed model.Experimental results show that the proposed model combines the advantages of the fourth-order isotropic diffusion equation and the fourth-order anisotropic diffusion equation,achieving a better tradeoff between noise removal and edge preservation.3.The iterative non-local means filter smoothes image features while removing noise because of the global decay factor.For this reason,using the Gabor-transform-based edge detector and the correlation coefficient,an adaptive iterative non-local means filter was presented.Firstly,the Gabor-transform-based edge detector was used to extract image features,and then an adaptive decay factor was designed according to the different image features.For the pixels in the edge region,a small decay factor was chosen to preserve details.For the pixels in the flat region,a large decay factor was chosen to remove noise.Furthermore,the correlation coefficient between patches was used to modify the Gaussian weighted Euclidean distance for the structure region pixels,which could improve the precision of Euclidean distance measurement and then effectively removed the noise in the structure region.Experimental results show that the proposed filter has a better edge-preserving capability,compared with the original iterative non-local means filter.4.On the basis of the research on the non-local total variation model based on the partial differential equation theory and the non-local means theory,a new non-local total variation model based on the block-matching and 3-D filtering(BM3D)algorithm was proposed for image denoising.Firstly,the preprocessed image was obtained with the BM3 D algorithm.Then,taking the place of the noisy image,the preprocessed image was used to construct the fidelity term of the energy functional and to design the weight function in the non-local total variation regularization term.Finally,the energy functional of the proposed model was solved by the split Bregman algorithm.Experimental results show that the proposed model is superior to the original non-local total variation denoising model in terms of visual effect and objective index.The advantages of the proposed model are more obvious,especially for the highly degenerated noisy images.What's more,the proposed model can effectively suppress the appearance of false information in the flat region,which overcomes the problem faced by the BM3 D algorithm.In addition,the proposed model can obtain the better denoising result for BGA solder joint X-ray images,and the superiority and practicality of the proposed model are further verified.