Sparse Decomposition Algorithms Based On Two-dimensional Image Can Not Be Separated Dictionary

Sparse image representation is a very significant task for image compression and transmission. Among all kinds of image decomposition methods, matching pursuit is very popular. The research on the human visual system shows that the image representation method with high performance should have such features as multiresolution, locality, critical condition, direction and anisotropy. Compared with the traditional image transformations with part of above features such as Fourier transformation and wavelet transformation, the 2D nonseperable dictionary used in this thesis answers for all of them. Therefore, based on the 2D nonseperable dictionary and matching pursuit, this thesis achieves both gray and color image decomposition. Its main contributions are as follows:1. The thesis deeply researched the features of the 2D nonseperable dictionary, concluded the relationship between the parameters of the atoms and the relative correlation of them.2. Based on the analysis of the 2D nonseperable dictionary, the researches on the full search matching pursuit algorithm and tree-based pursuit algorithm, the thesis proposed multiscale tree-structured dictionary which can be easily and effectively built, then achieved the multiscale tree-based pursuit. The algorithm with high performance and low computational complexity can quickly build the multiscale tree-structured dictionary. When compared with the tree-based pursuit algorithm, its advantages are obvious, include: 1) it is very simple to build a multiscale tree-structured dictionary– no requirement to compute the correlation of the atoms and the feature vector of a big matrix and no need to solve the computational problem; 2) it needs no extra memory– all nodes in the tree come from the original dictionary.3. The thesis researched and analyzed the RGB color space. The conclusion shows that RGB color space matches the features of matching pursuit, thus can be used as the main color space in the color image decomposition.4. The thesis proposed the multi-channel and multi-atoms matching pursuit algorithm based on the RGB color space to decompose the color image. No correlation of the channels is considered in this algorithm, thus each channel is decomposed independently. The algorithm has high performance owing to the independent decomposition of each channel. The main advantage of the algorithm is its good performance, and the shortage is in its high computational complexity.5. Enlightened by minimal residue energy matching pursuit algorithm, the thesis proposed the maximal residue correlation matching pursuit based on RGB color space. Compared with the method to choose the best channel of the color image in the minimal residue energy matching pursuit algorithm, the method in the maximal residue correlation matching pursuit algorithm matches the matching pursuit and RGB color space better. Although the algorithm does not constraint on the minimal energy directly, the optimal atoms chose by the algorithm is similar to the R, G, B channels of the color images in structure, thus it has high PSNR to some degree and better visual quality.6. Suggested by the minimal residue energy matching pursuit algorithm and the maximal residue correlation matching pursuit algorithm, the thesis proposed the single channel and single atom matching pursuit algorithm. Compared with the above two algorithms which find the best channel at each interation, it finds the best channel or computes the best representive signal once at the very beginning. Although the thesis does not know how to choose the best channel or compute the best representative signal, it finds out that among the R, G, B channels, one channel is the best channel for the color image in the decomposition at any time. And this result proves the effectiveness of the algorithm to some extent.