Image Codingand Denoising And Based On Sparse Representation

In signal analysis, it is always desirable to represent the signal in a compact way so as to reveal its essential features. Toward this goal, the sparse representation which describes the signal with as few elements as possible has been developed. As a new powerful method, the sparse representation has attracted much attention and had an important impact on signal processing and analysis. At present, it has been widely applied to many fields such as image processing, pattern recognization, and automantic measurement and control, etc.This thesis addresses the issues of sparse representation and its application to image processing. Surrounding the two main problems, dictionary construction and sparse decomposition, the image coding and denoising methods based on sparse representations over redundant dictionaries are deeply studied. The main contributions are as follows:1) A new fixed-point theorem with a variable parameter is presented. Based on this theorem, a novel controllable decoding scheme is developed for fractal image compression. The new scheme provides various progressive modes to meet the needs of different applications. The proposed decoder can be applied directly to the existing fractal compression systems without imposing any constraints on the encoding process.2) A new multiscale matching pursuit method for image approximation is proposed. In this method, the pursuit is performed at various scales and the task of scale transition is done adaptively. By exploiting the geometric properties of the dictionary, the target atom is built and extracted at the original scale. Consequently, the proposed method offers a reduction in computational complexity while maintaining the high performance of approximation.3) A novel matching pursuit (MP) image coding method based on block partitioning is proposed. By exploiting the energy and position distributions of MP atoms, the coefficient and position parameters of atoms are organized and coded effectively. The proposed coder achieves a significant improvement over the existing MP coder in both coding efficiency and scalability. Compared to other state-of-the-art coders, it offers comparable PSNR performance and better visual quality at low to medium rates. At the same time, the new coder has the advantage of producing highly flexible streams in terms of both rate and resolution scalability, which makes it very attractive for various multimedia applications over heterogeneous networks.4) A new denoising method using sparse representations over a global dictionary is proposed. This method improves the previous ones in two aspects: dictionary training and denoising. In the dictionary training, a two-phase dictionary training algorithm is proposed. By introducing a correlation coefficient matching criterion and a dictionary pruning scheme, the conflicting problems of structure extraction and artifact suppression are better tackled. In the denoising, a multi-stage sparse coding scheme is proposed to exploit the multiscale nature of the image and further reduce the artifacts. The proposed method achieves significant improvements over the previous sparse denoising methods and outperforms the state-of-the-art methods in terms of both objective and subjective quality at high noise level.5) A novel denoising method using sparse representations over a spatially adaptive dictionary is proposed. This method combines the ideas of non-local and redundant sparsity, and obtains the sparse image representation by training an adaptive sub-dictionary for each image patch. In the dictionary training as well as the atom selection, the strength of both the global and local subspace analysis is combined to overcome the problems of previous adaptive denoising methods. Compared to the methods using fix basis or dictionary to decompose the image, this method provides a local-adaptive representation and thus has the ability to better capture image details. Not surprisingly, the proposed method outperforms the state-of-the-art methods in preserving image details such as edges and textures.