Fast Algorithm For Image MP Sparse Decomposition Based On FHT And Core Dictionary And Its Applications

With the development of science and technology, human society gradually step into the information era, and makes the relate of images and video etc digital information and life becomes to closely gradually. Also requires a precise image representation methods which can accorded with human visionremains characteristics and efficient accurate, to process the data of image or video, so as to raise the performance of image compression and image magnification etc. Image sparse express overcome the disadvantages of orthogonal decomposition, and show many advantages which accord with human characteristics, concise and sparse etc, thus became a hot spot of image representation research. The matching pursuit is the most commonly used algorithm of image sparse representation, but because of the slow calculation, seriously hindered the matching pursuit algorithm's actual application.This thesis concentrates on the matching pursuit algorithm of large amount of calculation. We make deeply study for Fast Algorithm for Image MP Sparse Decomposition Based on FHT and Core Dictionary and it's application.Firstly this paper introduces the basic principle for one-dimension signals and two-dimensional image of matching pursuit algorithm, and gives the objective evaluation standard for image decomposition.Then, in order to improve the speed and the reconstruction quality in image sparse decomposition, In this paper, a fast algorithm for image MP(matching pursuit) sparse decomposition based on FHT(Fast Hartley Transform, FHT) and core dictionary is proposed. Firstly, this algorithm replaces the complete dictionary with the core dictionary in image MP sparse decomposition. Such operation can not only improves the speed of the dictionary forming, but also provides the possibility for the global search of the best atomic. Secondly the given image is converted to one-dimensional signal, and the atoms in the core dictionary which is the compact form of the common dictionary are also correspondingly turned into one-dimensional. Then cross-correlation between image or the residual images and atoms is calculated by one-dimensional FHT to find the best atoms. In conclusion, this algorithm can improve the speed of finding the best atom effectively. Compared with the common methods of image sparse decomposition, which are based on MP or genetic algorithm, this algorithm improves the decomposition speed and reconstruction quality efficiently under the same conditions. The results show the effectiveness of the proposed algorithm.Secondly the thesis analyses the meaning for the result of sparse decomposition. Image zooming algorithm for sparse decomposition based on core dictionary and FHT is proposed. This algorithm firstly decompose the magnified image used the fast algorithm for image MP sparse decomposition based on FHT and core dictionary. Then do the interpolation operation for the codfficient of tranlation and flexiable where the decompose results data. Finally obtained the zooming iamge using the interpolation of atomic parameters to reconstructed. This algorithm resolve the problem of edge blur, block-effect, Edge character and detail information lost etc in image interpolation zooming, and obtain the better quality of enlarge image.Final via analyzes the distribution rule and scope for the result data of sparse decomposition, this thesis proposed an image compression algorithm for sparse decomposition based on core dictionary and FHT. This algorithm firstly decompose the compressed image used the fast algorithm for image MP sparse decomposition based on FHT and core dictionary. Then do the pretreatment of sorting and prior difference for the sparse decomposition results parameters. Finally get the zip file via code the parameters after processed. This algorithm get the quality of uncompressed image than the quality of JPEG and JPEG2000 uncompressed image in low bit rate cases.