Research On Multiple Kernel For Sparse Representation And Dictionary Learning

In recent years, with the rise of compression perception, sparse representation has caused a large number of researchers interested in, and it has been successfully used in image restoration. Had been extracted from large data samples of complete dictionary, using sparse representation solve the problem of image processing has been very mature. However, how to effectively use sparse representation to solve the problem of pattern recognition has become a hot spot. Based on the sparse representation classification (SRC) is put forward, the sparse representation in the application of pattern recognition has been entering a new chapter. In sparse representation based classification, composed of all the training samples from choose the representative elements as a set of complete dictionary base, base linear table and the test sample can be made of the group, said its coefficient is sparse. Sparse coefficient is obtained by minimize th ι0 -norm or ι1-norm, so as to classify the test sample according to the sparse coefficient. Despite sparse representation has achieved good results in this respect, but in the original when choosing the training sample may not be accurate, to produce large deviation in the expression of the test sample. Therefore, when using the sparse representation in the case of the necessary, it will need a dictionary by learning the training sample. At the same time, due to the kernel methods in such aspects as the SVM, PCA, the FDA showed great advantage in the use, kernel function method has attracted great attention. It is mapped to high-dimensional data from the original space makes the data in high dimensional space can have greater distinction, it can achieve precise representation. Therefore, in this thesis, the sparse representation and dictionary learning are studied, and the two types of problems to establish effective kernel function method. In order to make full use of the kernel function information, respectively structure the multiple kernel sparse representation based classification and the dictionary learning based on the multiple kernel.The content of this thesis is summarized as follows:(1) To the lack of significant based on sparse representation classification criterion, the multiple kernel sparse representation (MKSR) is put forward and used in the classification problem. We can adopt a simple iterative algorithm solving sparse coefficient, thus sparse coefficient can be obtained and at the same time the rationality of this iteration formula for theoretical proof is given. On the weight of the multiple kernel issues, it can not only make the weight update automatically, but also present two different weights updated ways and analyzed respectively. The experimental results show that the multiple kernel sparse representation based classification recognition rate relative to the sparse representation based classification recognition rate has great improvement, even take the weight of the second kind of multiple kernel sparse representation based classification has the optimal classification performance.(2) In order to improve the classification performance of the dictionary learning in classification problem and take the most use of the nonlinear structure, the dictionary learning based on the multiple kernel(MKDL) is put forward and used in the classification problem. In sparse coding phase, the multiple kernel function is added to the orthogonal matching pursuit algorithm which is used to solve the sparse coefficient and thus form the multiple kernel orthogonal matching pursuit algorithm. In dictionary updating phase, according to solving the sparse coefficient, add multiple kernel function in the KSVD to update per column of dictionary named multiple kernel KSVD. Repeating the sparse coding phase and the dictionary updating phase can get the updated sparse coefficient and a dictionary. Experimental results show that the classification performance of the dictionary learning is better than the performance of KSVD. At the same time, the classification performance of the dictionary learning is outperformance than the kernel dictionary learning using a single kernel.