A Study On Algorithms Of Image Restoration Based On Sparse Representation And Matrix Completion

Image restoration is one of the widely used branch of image processing in modern society,the development and progress of which is closely relat-ed to daily life.This paper mainly studies restoration algorithms for nat-ural images,including sparse representation based image super-resolution reconstruction and matrix completion based image denoising.The model of original image reconstruction based on sparse representation may cause many different problems when it comes to process different instances,so we need to improve the model and enhance the effect of the reconstruction;similarly,image denoising algorithm based on matrix completion also need to improve,in the face of different noise,even the mixed noise,it is very necessary to enhance the effect of image denoising.This dissertation is devoted to sparse representation theory and matrix completion theory,developing the research on image super-resolution re-construction algorithm based on adaptive sparse representation,research on super resolution reconstruction algorithm based on non local structure similarity and edge sharpness dictionary,research on super resolution re-construction algorithm based on non local structure similarity and local linear projection and research on weighted low rank matrix completion al-gorithm based image denoising with mixed noise.The specific content of the work is described as follows:1.For super-resolution image reconstruction,the l1 and l2 regulariza-tion can represent sparsity and coordination of sparse representation sepa-rately,and the former can embody the sparsity of coefficient well,the lat-ter reflects weak sparsity and can accelerate the speed of operation greatly.In order to reconstruct the image better,we need to balance the role of sparsity and coordination,so that it can produce the best reconstruction ef-fect adaptively along with the change of the dictionary.This dissertation proposes a super-resolution reconstruction model based on adaptive sparse representation(ASCSR)by constructing a new regularization term.The model can integrate sparsity and coordination into a regularization term,and emphasis on sparsity or coordination according to the change of dic-tionary,and produce most suitable coefficients through the coordination of the two property.As to the solving of the model,we use the alternating direction method of multipliers(ADMM)to solve the optimization mod-el.Compared to some existing super-resolution reconstruction method,our ASCSR method has better reconstruction effect,and better stability for the change of dictionary and anti-noise property.2.Due to the non local similarity of the patch,we propose an image re-construction model based on non local structure similarity and edge sharp-ness dictionary.First of all,all the training patches should be classified into different categories by the difference of edge sharpness of different patch;secondly,we train several dictionaries for different types of training patches;afterwards,we add a non local structure similarity constraint into our model,and then select the most suitable dictionary to reconstruct cur-rent patch,and the current patch has the strongest similarity to the training patches which is used to train most suitable dictionary,alternating iterative method is used to solve our reconstruction model in this paper;finally,the corresponding high resolution image can be obtained by integration of re-constructed patches.Based on the edge sharpness dictionary and the non local similarity constraint,our proposed NLSS-ESD method realizes the better reconstruction effect than some other methods indeed,and the use of the edge sharpness dictionary training model also greatly reduces the training time of the model.3.Because of the sparsity of the patch of low resolution image and the high resolution image,this dissertation proposes a local projection super-resolution reconstruction algorithm based on non local structure similarity and sparse preservation.The key point of this method is that some local and non local patches of the same or different images is similar in some respects,and we can get a high resolution patch by the function of a linear projection from the low resolution patch.This dissertation uses structural similarity and sparsity to classify the patches of training set,then learning the sparse coefficient matrix for corresponding kind of patch,and obtaining the projection between the patches on the basis of coefficient matrix.The coefficient matrix is obtained by the cooperative representation model,and the projection learning model also includes such a coefficient matrix in or-der to preserve the sparsity and cooperativity.After learning the projection for each class training patch,we can reconstruct each test image through the simple linear projection.The contrast experiment shows that the numerical results and visual effects of our proposed model are effective.4.Based on the low rank property of the matrix which is composed of several similar patches,this dissertation proposes an image denoising algo-rithm for mixed noise based on weighted low rank matrix completion.In general,the kernel norm of the matrix can not reflect the low rank property of the matrix well,in order to reflect the low rank property of the matrix better and obtain a better denoised image,we propose a weighted matrix model.This method picks up similar patches by using of the patch match-ing to form low rank matrix,and forms the low rank matrix with missing entries according to the properties of similar patches and the columns of low rank matrix,and then restores the original low rank matrix image by using weighted low rank matrix model to achieve the purpose of denoising.Our method transforms the denoising problem of patch caboodle into the problem of matrix completion,and the weighted kernel norm is used to op-timize the low rank matrix.The finishing of matrix completion means that we have removal image noise.The comparative tests show our proposed method has good numerical effect and visual effect for different images and different noise species.