Minimum Dictionary Learning Based On Non-local Sparse Model

With the development of computers and the arrival of information age, the practical demand for using computer to process image is growing daily. As one of the most important components of t image preprocessing, image denoising affects the subsequent operations. Under the framework based on the local dictionary theory, this paper analyses on the summarizing the relevant research both at home and abroad, design a minimum dictionary based on non-local and Competitive Agglomeration for denoising algorithm according to the additive white gaussian noise characteristics. At the same time, we utilize the geometrical properties of space to build a minimum local dictionary, we use minimum local dictionary for image reconstruction experiment. At last, we analyze the advantages between minimum local dictionary and other dictionaries.The main work of this paper consists of the following three parts:Firstly, this paper elaborates the development history and the theory model of sparse representation(SP) in detail, and does a analysis of all kinds of sparse decomposition algorithm and dictionary learning algorithm applied to image denoising problems.This paper introduces the synchronous orthogonal matching pursuit algorithm(SOMP) systematically, introduces the advantages and disadvantages of various types of dictionary use in image denoising in detail.Secondly, by introducing competition agglomeration(CA) algorithm this paper proposes the minimum dictionary which is based on non-local joint sparse and K-SVD algorithm. We obtain the similar set according to the non-local sparse model, obtain the K-SVD dictionary by singular value decomposition cooperation to the different similar sets, we can find the optimal segmentation and the optimum number of clusters of a given data set by CA clustering algorithm. We update the dictionary by remove rarely used duplicate or similar elements. This paper proposes a natural image denoising method which is based on the non-local sparse K-SVD dictionary and CA competition agglomeration. The algorithm makes the size of the dictionary atom is optimized, while meets the similarity of the characteristics of the image information from.At last, this paper proposes a minimum local dictionary based on nonlocal joint sparse model and geometrical properties of space. In order to take advantage of the global self-similarity of the image, this algorithm uses joint sparse representation model constrained image similar content so that it has a similar sparsity. We use the self-similar information of image block, through the joint sparse representation so that it can maintain the similarity of related information in the sparse domain. By introducing the principle of locality constrained linear coding(LLC), and improving to the local dictionary singular value decomposition(SVD), The dictionary atom is similar to local signal. A natural image denoising method is proposed based on the new local dictionary and the nonlocal constraint of representation coefficients. Experiments prove that the method for image reconstruction have good results.