The Methods And Applications For Image Processing Using Sparse Representation And Optimization Theory

As the advancement of Compressed Sensing（CS） theory, the sparse representation and optimization theory and its applications obtained vigorous development. It has achieved some important practical systems, such as single pixel camera, single pixel quantum imaging, etc. Besides, it also has a large number of applications in each stage of computer visual perception system, including image restoration, medical and radar imaging, remote sensing, classification and recognition of texture and target, image analysis and image fusion, visual detection and tracking etc.. The researchers have confirmed that the image signals have sparse characters in spatial domain or transformed domain. Based on the principle of CS, the thesis makes use of the advantages of sparse representation and optimization in image signal processing. The thesis focuses on visual perception problem in computer vision. The main work and innovations are as follows.（1） The research of local and nonlocal sparse representation model for image restoration. At present, the models of image restoration are divided into local and nonlocal classes based on sparse representation and optimization theory. There are some recovery methods combining with local and nonlocal model. This paper conducts in-depth analysis and systematic research about the problem. In the implementation of well known K-SVD method, it is easy to fall into local minimum problem. In the stage of sparse representation, the ?₀ norm is solved by greedy pursuit method. Here, the paper puts forwards that the greedy pursuit method is substituted by the fixed point continuation using the ?₁ norm convex optimization methods. Then the sparse representation coefficients are obtained by above algorithm. In the clustering based sparse representation method, the new surrogate function is defined for the solution of double ?₁ norm model. The parameters are updated alternately by the surrogate function. The convergence character of the agent function is also analyzed. By the optimized solution iteratively, the error of image restoration can further be reduced and better restoration performances.（2） The visual fusion perception based on sparse representation and optimization. The importance of image fusion is self-evident. In the acquisition of images to be fused will be inevitably disturbed by various degradation factors. Researchers want to develop fusion methods that can remove degradation factors（such as noises, blurring effect, etc.） or super resolution simultaneously. The paper presents an image fusion framework based on online dictionary learning（ODL） in pixel level. The ODL is adopted to learn a sparse and redundant dictionary from image blocks to be fused. The ODL does not need to learn all the data again in the process of updating dictionary. It is suitable for processing large amount of data with high computational efficiency. Secondly, the paper considers both the value of sparse representation coefficients and the information entropy in the determination of fusion rules for sparse representation coefficients of fused image. The weights of fusion coefficients are computed by information entropy. The fused coefficients are determined according to different conditions. Then, the fused image is restored according to learned dictionary and fusion coefficients. The fusion experiments on two modal images indicated that the fused images by the proposed fusion framework contain more significant features and abundant information. The objective evaluation index is also better.（3） The object classification and recognition based on weak sparsity constraint. In the issues of classification based on sparse representation, which provide more help for upgrading the performances of classifier, sparse constraints or collaborative representation? In this paper, the ?₂ norm with weak sparsity constraints is used for solving the sparse coefficients instead of ?₁ norm constraints. It is combined together with discriminative model in a unified framework. The paper proposed an effective method for face recognition and object classification, called Discriminative and Collaborative Representation（DCR）. First of all, all the training samples is used for representing the test sample by collaborative representation way in DCR method. The collaborative representation has robust character to occlusion or other degradation ingredients. In additional, the combination of discriminant model with collaborative representation can provides more discriminant information for classification and recognition. The proposed framework mines the similarity and identification among samples effectively. Compared with other existing methods, the proposed method has comparative experimental performances. At the same time, the experiments show that the classification error has more effects on object classification than the representation coefficients. This idea provides a way to explore the universal feature selection mechanism.（4） The method of manifold learning based on sparse representation and feature dimension reduction. Sparse preserving projection（SPP） method preserves the sparse reconstruction relationship among sample data by minimizing the ?₁ norm regularization term and its related objective function. Inspired by this, the paper proposed a sparse preserving projection method based on non-similarity among samples as an extension of SPP. The relationship among samples is calculated according to projection vector, representation coefficients and reconstruction error. Then, the dissimilarity scatter matrix is build up among all the samples. The linear transform is derived by maximizing the corresponding objective function. The linear transform can preserves the dissimilarity of original data in low dimension space. Aiming at the preserving projection process, the null space of denominator contains important identification information which is discarded directly in the PCA stage. Inspired by the idea of diagonalization simultaneously, a direct and complete solution is given. The proposed method does not have to set the neighborhood size and the heat kernel width of the proposed method. The experiments on some benchmark datasets show the effectiveness of the proposed method.