Research Of Low-Rank And Sparse Regularization For Image Denoising And Segmentation

With the development of compressive sensing,low rank and sparse regularization model-ing has gained great success in the fields of image processing and computer vision.Both image denoising and image segmentation are fundamental and very important problems in the fields of image processing and computer vision,whose results have significant influence on successive processing,such as image analysis,image understanding,object recognition,and so on.Image denoising aims to restore the real clean image from its noise-corrupted observation while preserving image features as much as possible.The goal of image seg-mentation is dividing an image into several regions with specific visual semantic according to the similarity and difference of image feature.In this dissertation,we devote ourself to researching on both image denoising and image segmentation problems via employing the low rank and sparse regularization.For image denoising,we make deep analysis on the structure of a cluster of similar patches,and propose three low rank regularization image denoising approaches based on different priors on a cluster of similar patches.For image segmentation,we transform it into the clustering problem of image feature,and present t-wo image segmentation methods based on improved sparse subspace clustering.The main contributions of this dissertation lie in the following folds:1.Based on the analysis of the structure of the similar patch matrix?SPM?,a novel image denoising method named low rank representation?LRR?with cluster adaptive dictionary is presented by using the row correlation of the SPM.On the one hand,we impose low rank regularization on the row coefficient matrix of the SPM under a cluster adaptive dictionary to recover the correlation structure of the SPM inherent in clean image.On the other hand,a cluster adaptive dictionary is learned to represent each SPM so as to sufficiently exploit the underlying structure of the similar patch cluster.An efficient alternative minimization algorithm is derived to solve the proposed LRR model by applying variable-splitting and penalty techniques.Numerical experimental results demonstrate that the proposed LRR method achieves a competitive denoising performance compared with state-of-the-art de-noising methods in terms of both quantitative measures and visual quality.2.Based on the further analysis of the structure of the SPM,a new image denoising method called bidirectional low rank representation?BiLRR?with cluster adaptive dictionary is pro-posed by utilizing both the row correlation and the column correlation of the SPM.We impose low rank regularization simultaneously on the coefficient matrixes of column rep-resentation and that of row representation to recover the correlation structure of the SPM inherent in the clean image.Meanwhile,a cluster adaptive dictionary is learned to code each SPM so as to well preserve the fine structure of image.By applying a variable splitting and penalty technique,we present an efficient alternative minimization algorithm to solve the proposed BiLRR model.Experimental results indicate the proposed BiLRR method achieves a competitive denoising performance in comparison with state-of-the-art denoising algorithms in terms of both subjective and objective qualities.3.Based on the fact that image patch taken from a clean image lies in a low dimension-al subspace,a novel image denoising method named two direction low rank representation?TDLRR?with a pair of row and column low rank dictionaries by employing both the row correlation and the column correlation of the SPM.Low rank regularization is simultaneous-ly on the coefficient matrixes of column representation and that of row representation.The underlying image is constructed by exploiting two direction correlation structures inherent in natural image,which leads to restoring a better low dimensional subspace structure,and suppressing the noise of image effectively.Next,the augmented Lagrangian method and the alternating direction method are applied to solve the proposed TDLRR model.Numerical experiments indicate that the proposed TDLRR method achieves a competitive denoising performance in comparison with the state-of-the-art denoising algorithms in terms of both subjective and objective qualities.4.To overcome the disadvantages of existing models,we defined a novel sparse measure??l_p,1norm.A improved sparse subspace representation model is proposed by taking the l_p,1norm as sparse regularization.The representation coefficient matrix obtained from this new model is not only inter-cluster sparse but also uniform intra-class,and it can fit the subspace structure of data well.We present a effective algorithm for solving the proposed model,and introduce a improved sparse subspace clustering method.Transforming the im-age segmentation problem into the clustering problem of image feature data,we present a novel image segmentation method based on the proposed improved sparse subspace clus-tering.The image to be segmented is first over-segmented into some uniform sub-regions called superpixels,and color histogram of each superpixel is computed as its feature.Then superpixels are clustered by employing the proposed improved sparse subspace clustering,whose result is the image segmentation result.Experiments on data clustering and image segmentation show that,the proposed improved sparse subspace clustering method has sat-isfied clustering performance and is robust to noise.It can obtain satisfied segmentation results for natural color images.5.To remedy the shortcoming of over-sparse in the sparse subspace clustering methods,we present a new correlation guided sparse subspace representation model by explicitly exploring the correlation among data points.The representation coefficient matrix gained from this new model is guaranteed to having grouping effect within cluster as well as sparsity between clusters.So it is able to reveal the true subspace structure of data.We present a effective inexact augmented Lagrangian algorithm for solving the proposed model,and introduce a correlation guided sparse subspace clustering method.Image segmentation can be transformed into the clustering problem of image feature data,therefore we present a novel image segmentation method based on the proposed correlation guided sparse subspace clustering method.Numerical experiments on data clustering and image segmentation show that,the proposed correlation guided sparse subspace clustering method has excellent data clustering and image segmentation performance.