Research On Image Denoising Algorithm Via Graph Filtering Optimization

Image denoising is a fundamental and important research field in image signal processing.Since the development of image denoising accompanies with the theory breakthrough of signal processing,various theories nowadays provide the great potential opportunity to promote the quality of denoised image into a new level.To this end,this dissertation tries to deal with image denoising problem through some recent graph signal methods,specifically by graph filtering.Therefore,image denoising via graph filtering is carefully studied from several aspects,i.e.,graph filtering practicality,adaptive graph filtering and subspace image filtering.As a result,the denoising performance is well improved and can be competitive with the state-of-the-art image denoising algorithms by model-based learning and deep learning.Additionally,since I have engaged in the classification of mental diseases by using the graph regularization method as a visiting student abroad,I also introduce the related work here.The main contribution of this dissertation is summarized as follows.1.We propose a hybrid denoising algorithm with the analysis of several existing image denoising algorithms.The proposed algorithm fully employs the prior of image patches,where noisy patches are identified into different categories by their attributes and then cast into the corresponding denoising methods.This operation makes different kinds of patches better restored by taking advantages of each denoising method.In details,our hybrid algorithm divides image patches into four categories such as flat,edge,texture and detail patches by their corresponding block and patch analysis.Then the patches in each category carry out their denoising procedures respectively to improve the denoising performance.2.As for graph-filtering-based image denoising,we present an adaptive graph filtering algorithm to tackle the empirical graph eigenvector setting problem,where an auto-selection eigenvector strategy is incorporated to fit for different images under various noise levels.In this algorithm,an optimization model of rough estimated image is firstly established with noise estimation,wherein the number of eigenvectors is controlled by the given noise threshold.As a result,the intermediate image is generated with the rough image.A group sparse model is sequentially employed to select the eigenvectors of intermediate image.Meanwhile,the denoised image is obtained under the control of noise threshold in the group sparse model.In brief,the proposed adaptive graph filtering denoising algorithm only depends on the noise level rather than the empirical graph eigenvector selection.Experiments show that our algorithm achieves the comparable denoising performance with the traditional graph filtering.More importantly,it greatly increases the practicability of graph filtering.3.Since the traditional graph filtering belongs to a bisection low-pass filtering method,it seems less effective to deal with the noise of whole band.An adaptive spectrum weighted graph filtering method is given to solve such a problem.Here,we present a patch-based denoising algorithm that is inspired by the existing low rank denoising model named as ARLLR.An adaptive coefficient shrinkage strategy is designed in the graph frequency domain,where the full-band filtering is theoretically realized.Meanwhile,the well-known ARLLR model is also included in our graph filtering framework.The proposed algorithm provides a well theoretical explanation of graph filtering,whereas its denoising performance is slightly inferior to ARLLR.4.To further promote the denoising performance of graph filtering,we present two improved version,i.e.,adaptive spectral weighting algorithm with pixel smoothing and its regularized pixel smoothing approach.The former algorithm uses super-pixels to learn the graph structure and thus obtains the graph eigenvector for graph filtering.It not only considers the relationship among patches and pixels of patch,but also makes full use of the advantages of graph structure.As a result,it achieves the better denoising result than that of ARLLR.Moreover,it can also be compared with several deep learning denoising methods.In the latter algorithm,a guided-patch regularizer is incorporated.In detail,the guided patch is achieved by a maximum aposteriori probability estimator,which is helpful to rebuild denoising images.Experiment shows this algorithm outperforms most state-of-the-art model-based methods and is competitive with some deep-learning methods.5.Considering the patch group is a ‘fat' matrix that fits for subspace graph filtering,some subspace graph filtering approaches are proposed.Given a fat data matrix,we prove that its eigenvector matrix achieved by the extended SVD model is equal to a graph eigenvector matrix of subspace graph filter.Then,a subspace graph learning model is established to find a set of optimal graph smoothing bases in the given subspace.With these graph bases,the signal representation can be well performed to meet the graph smoothing requirement.The results show that,although the signal reconstruction efficiency in the graph smoothing subspace is lower than that in the eigenvector space obtained by the traditional SVD decomposition,its denoising performance is better.It solidates the theoretical fundament for the subspace graph filtering denoising.6.We use some approaches of graph signal processing in the field of mental disease classification,especially in the classification of Attention Deficit Hyperactivity Disorder(ADHD).The brain functional connectivity data is employed as target data to separate ADHD patients from healthy controls.We propose a dual subspace learning method for ADHD classification,where a graph regularization term is incorporated to improve the classification performance.In details,an improved graph Laplacian matrix is designed to enhance the relationship among the features within groups.Moreover,a binary hypothesis framework is introduced to give a hypothetical label to test data.Subsequently,binary labels affect the performance of feature extraction and subspace learning of the training data.Finally,the label decision of test data is provided by comparing the subspace energy under different hypotheses.The experiments on various databases show our method achieves a better performance than those of existing classification methods,where the average accuracy is 88.1%.