Fractal Image Compression Based On Wavelet And Entropy

The fractal image compression is one of the second image coding methods, which attracts many people's attention. The fractal image compression is based on Iterated Function System (IFS) and Compression Mapping Theorem. Jacquin's coding scheme is based on the block matched, and the process of it wastes time very much, which is the biggest obstacle that hinders the fractal image compression. The major work of this paper is to introduce the entropy and the wavelet transform while not reducing the image quantity. The major work of this paper is as follows:1,Summarize the development process of the fractal image compression, the difficulty and shortcoming of the image compression and the current study state. Expatiate the theory foundation of fractal image compression, especially the fixed point theorem of compression mapping and collage theorem.2,Introduce the entropy to the fractal image compression, then calculate the entropy of every image block , match the range and the domain according to the entropy and look for the similar block. Only rotate and folio transform is needed for the domain matched by entropy because of the property of rotation and folio transform invariance of entropy, which greatly reduce the coding time. The result of the numerical experiment shows it.3,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, only fractal image compression in the low frequency is needed. Firstly, the low energy image is coded by the improved conventional image compression coding method. Then the low energy image is coded by the fractal image compression coding method based on entropy. The numerical experiment results show that the coding speed is improved greatly.