Combining Fractal With Wavelet Transformation In Image Compression

Nowadays, much attention has been paid to two research branches in the field of image compression, that is, fractal coding and wavelet transformation coding. In particular, the hybrid algorithms of fractal and wavelet transformation coding have already been developed and are becoming popular. In this paper, we make some improvements on the application to image compression of the three research branches mentioned above .1. It is well known that the encoding time to search matching domain block for every range block is definitely long and encoding speed is accordingly rather slow. In order to overcome such a problem, we propose and implement a parallel fractal encoding algorithm by utilizing the factor that one can search the matching domain block for every range block independently. The speed of the parallel scheme is nearly 4 times faster than that of the scheme proposed by Fisher with almost the same compression ratio and reconstructed image quality.2. We put forward a zerotree wavelet image compression algorithm with rigid package length which based on EZW (Embedded Zerotree Wavelet encoding algorithm). At first, the datum of the image are turned into many zerotrees which consist of wavelet coefficients by using zerotree wavelet image compression algorithm. Then, those zerotrees are put into many packages with rigid package length. Because the data packages produced by the algorithm can be decoded independently, error or missing of some data packages will not affect other data packages. As a result, the method is suitable for image data transmission in the network.3. As is well known, in the general combining algorithm of fractal and wavelet transformation applying to image compression, one could product many subbands including one low frequency subband and several high frequency sub-bands after transforming the image by two-dimensional wavelet transformation one or more times. The similar high frequency subbands are assigned to en-code by fractal coding algorithm. This algorithm has one advantage with highcompression ratio, whereas it has one shortcoming with relatively slow encoding speed. In this paper, we propose the parallel hybrid algorithm of fractal and wavelet transformation, which is showed that, it can improve the encoding speed by experimental results.