The Research And Application In The Field Of Image Compression And Coding By Wavelet Transform And Fractal Theory

One of the primary problems we are confronted in the digital information age is how to store and transmit huge amounts of images and videos effectively. The speed and methods of image compression are developing quickly. Some international standards such as JPEG,MPEG,JPEG2000,H.26X and so on have been made. But the CR(compression rate) and the time of encode-decode are not so perfect and need to be improved. The classic source compression algorithm begins with the Shannon's information theory which doesn't utilize the HVS characteristics, and the CR is saturate about 10:1.Wavelet transform coding can remove the statistical redundancies in images effectively, at the same time, its property of multi-resolution transform adapts to HVS (human visual system) very well. FIC(fractal image compression) takes advantage of self-similarities which exist in the image commonly, It uses the self-similarity in different scales of image to find the corresponding fractal description and remove the geometry redundancies. FIC is one of the most competitive schemes in recent research, and it has the capable of achieving good image quality at a very high compression ratio.At present, there are many algorithms based on the wavelet transform and fractal compression, and the main thought is to decompose the image in multi-level by wavelet; and then code the part of low frequency or the high frequency with fractal image coding, or both of them, other points of views can be combined. Image compression and coding by wavelet transform and fractal theory is the primary problem at present. Many scholars are paying highly attention to the CR and the coding in order to make a great breakthrough.This paper do many and further research on the wavelet analysis, fractal theory and the application of them, and propose a method of fractal compression based on the wavelet transform. It decompose the image with 4 levels by Daubechies9/7, code the low frequency with self-adapting arithmetic and the high with fractal predictive coding, and utilize the variance contrast when compute the domain range .Finally, an experiment result which based on the MATLAB7.0 is proposed to prove the rationality.