Image Restoration Based On Nuclear Norm And Diffusion

Images as the carriers of information and transmission are the master sources for human being to obtain the information of environment.It affects the human production activities in all aspects,which may be small as our regular life,or as large as the aerospace industry.Image restoration is in a low level for image processing,and plays a significant role in many applications,such as computer vision,machine learning and artificial intelligence.The dissertation takes the images corrupted by Gaussian white noise or by impulsive noise as research objectives,and aims to improve the quality of restored image as far as possible.The theories of weighted nuclear norm low rank approximation and diffusion mode are adopted to the research on image restoration.The main research works and contributions are as follows:(1)To address the problem of how to characterize the weights in weighted nuclear norm regularization model,this dissertation proposes a method of characterizing nuclear norm weights with odd polynomial coefficients.An optimizing shrinkage curve algorithm(OSCA)is proposed for weighted nuclear norm minimization and is adapted to image denoising.In this optimization,the objective function is the Frobenius norm of the difference between a latent matrix and its observation.To obtain its solution,odd polynomial coefficients are used to characterize the weights of nuclear norm fully,and then the Frobenius norm of the penalty function is converted into the corresponding spectral norm.As a result,the parameter optimization problem can be easily solved by using off-andshelf plain least-squares.To improve the performance of the proposed algorithm,a matrix set is built,in which each matrix is established for similar patches extracted from noise image,based on local self-similarity in images.These matrices are termed Rank-Ordered Similar Matrix(ROSM).Experimental results show that the performance of proposed algorithm outperforms the state-and-arts algorithms,such as bilateral filtering and BM3 D,and also demonstrate that the proposed algorithm is effective and feasible.(2)The PM diffusion method often introduces excessive smoothing and can result in extensive visual feature blurring and thus are suitable only for images with low noise.A modified PM diffusion method to suppress salt-and-pepper noise is proposed to overcome these limitations.In contrast to the PM method,the modified PM diffusion method devises a noise detection to identify noise and only treats noisy pixels,which is similar to the switching filtering.Moreover,it diffuses along eight-neighbor directions,rather than along four-neighbor directions for the original PM diffusion method.Therefore,the modified PM diffusion method is suitable for images not only with low noise but also with high noise,and can reconstruct more details from noisy images,because of the both modifications.Experimental results show that the modified PM diffusion algorithm can achieve better results than the original PM diffusion,and can reach the performance of the state-and-arts algorithms,such as median filtering,switching median filtering,spectral gradient method.(3)The total variation diffusion method often introduces staircase effect,and are suitable only for images with low density noise.To overcome the limitations mentioned above,this dissertation proposes an improved total variation diffusion method,which divides pixels into different categories based on different noise characteristics.If an image is corrupted by salt-and-pepper noise,the pixels are divided into corrupted and noise-free;if the image is corrupted by random valued impulses,the pixels are divided into corrupted,noise-free,and possibly corrupted.Pixels falling into different categories are processed differently.If a pixel is corrupted,modified total variation diffusion is applied;if the pixel is possibly corrupted,weighted total variation diffusion is applied;otherwise,the pixel is left unchanged.In addition,the divergence operator employed in the improved total variation diffusion method is discretized via the central derivative at half pixel resolution,and thus it is rotationaly invariant for the angle of degree 90.Therefore,the improved total variation diffusion method is suitable for images with high density noise,and has the better accuracy and the stronger robust.(4)Two basic facts for corrupted color images are taken into account,i.e.,first,each channel in a color image is contaminated independently by noise,and contaminative components are independent and identically distributed;second,in a natural image the gradient fields of the channels are similar to one another.Based on the twofold,a decision-based marginal total variation diffusion method to suppress impulsive noise in color images is proposed.The new method not only implements the diffusion operation dependently in separate channels,but also improves the diffusion operation contrasting with the decision-based total variation diffusion.The decision-based total variation diffusion method treats each component equally.In other words,in each iteration of the algorithm,it treats different category components at once.In the new method,a hierarchical scheme is adopted.The new method first process the corrupted components,and then the possibly corrupted ones.Experimental results show that the new method achieves PSNR 1.5-2.5dB improvement over the former.(5)The total variation diffusion is only along the direction perpendicular to the gradient while not across in the gradient direction,which leads to that it is edge-preserving.Since the advance of the total variation diffusion,the coupling-channels diffusion method extends its application to color images.The coupling-channels diffusion method employs the variation matrix proposed by Di Zenzo to obtain the ”mult-valued gradient” of a color image,and then the diffusion operations in separate channels are along the direction perpendicular to the multi-valued gradient,while not across the direction of the multi-valued gradient.Otherwise,to further understand the rules of coupling-channels diffusion,the differences between the marginal diffusion and coupling-channels diffusion are analyzed.This analysis indicates that the marginal diffusions are along the independent direction perpendicular to the true gradient of each channel,whereas the coupling-channels diffusions are along the same direction perpendicular the ”fitted gradient”.In addition,considering the gradient fields in every channel in a color image are similar to one another,a conclusion is drawn that the marginal diffusion is an approximation to coupling-channels diffusion.Experimental results confirm this conclusion.