Image Compression Based On Fractal Theory

The data of images use is very huge, and bring a lot of trouble to it's storage and transmission, so one of the primary problems is how to effectively store and transmit huge amounts of digital images and videos. The fractal image compression coding method thoroughly brake through the theoretical framework of traditional coding methods and it gets more and more attention by it's benefits of potential high compression ratio, the decoding feature of independence of resolution, favorable reconstructed image quality and so on. The fractal image compression is concerned as the most promising method in image compression field.This thesis briefly introduces and summarizes image coding methods and reviews the generation and development of fractal image encoding. It systematically discusses the basic theories of fractal and the specific parts used to compress image. The paper introduces the classic Jacquin algorithm in detail and does the simulation. The simulation result shows that the sizes of rang block and domain block are closely related to the compression ratio and the reconstruction image quality. The bigger blocks get greater compression ratio and shorter decoding time, but the distortion increases with the bigger blocks as the same time.The traditional method of fractal image coding has many disadvantages and the long time of coding is the main problem. We introduce a quadtree-based algorithm for improving the fractal image coding time. The algorithm makes the range blocks quadripartition by testing to see if it meets some criterion of homogeneity. Compared with classic algorithm, the Theoretical and experimental results show that the proposed algorithm can almost achieve the same reconstructed image quality as the traditional classic algorithm, and can markedly reduce the encoding time and advance the compression ratio.We use wavelet transform to improve the encoding speed of the fractal quadtree-based image compression and a new algorithm Quadtree fractal coding based on wavelet transform. Decompose the image into high frequency part and the low frequency part by the wavelet transform. Because the energy concentrates on the low frequency part, it is seen as the attract factor of encoding image and only fractal image compression in the low frequency. We make the fractal codes that get from the low frequency appropriately scale transforms and then acquire the encoding image's fractal codes. The numerical experiment results show that the coding speed is improved greatly.