Many works of compressing image based on Wavelet transformation have been presented in recent years. Also, the method from Fractals is used in this field. First one is using of the pyramid subband decomposition, second takes advantage of self-similarity between the basic image and subimages. We combine these hNo kind of methods as a hybrid algorithm to complete compression of image. The experiments shown that this method has better performance than many others, especially, in the high compression ratio situation. A comparison with the famous EZW algorithm shows that its performance is close to the EZW algorithm. Introduc tionThe technique of image compression has been quickly developing since JPElG was proposed. Especially, in recent years marly works of image compression based on Wavelet Transformation and Fractals respectively reported. Definitely, The wavelet and Fractals are very useful tools for image compression. In the predictable future the JPEG must be replaced by other standard. The reason is that if we want to get high compression ratio with acceptable image quality, the JPEG in which the main technique of encoding is Discrete Cosine Transformation (DCT) is impossible according to amount of experiments. Many works based on wavelet transformation shown the result that in the case of compression ratio is less than 16 then there are not obvious difference between the reconstructed images using of DCT and 7NT respectively, 0-7803-291 2-0 but in the case of compression ratio is bigger than 30 the differences between reconstructed images are quite visionable. JPEG has two main drawback, one is block effects which is from DCT, the another is big errors due to Vector Quatization (VQ). DCT is operated on the small block of 8x8 pixels of the image, this is a spatial transformation, but not in the frequency area. However, th transformation is a spatial--frequent mation. It operates on the whole image and results in the components in different bandwidth. VQ essentially is a finite classification of m-dimensional sample space. In order to give a finite good classification with small diameter in each class, that means small distortion in the reconstructed image, then the codebook will be very huge. In fact, there is a big redundancy of codewords for a specific image. Basically VQ is a probabilistic type encoding, so it is a better encoding method if we know the probabilistic distribution of the images. As mentioned in many works, that is impossible to know the probabilistic distribution of the images. So, we need other encoding method for image compression. Fractals is a very usefhl tool to deal with .the self-similarity problem. If we ignore the , time-consuming searching process, the encoding method is more reasonable than VQ. So far, the EZW (Zero Tree Wavelet) [ 13 method is the best in the high compression ratio situation that the reduction of PSNR is almost linear with increase of compression ratio. We have repeated the experiment and have got very close result (see section 5). In this paper we propose a hybri...

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