Research On Fast Fractal Image Compress Coding

With the development of information network, the digital image information, as one of the most important information, is widely used. However, how to compress and store large amounts of image information effectively should be the hot issue of the studies. Fractal image coding is a type of new compressing technology, which is fairly promising and has huge application value. And then, fractal image compression technology is focused on by a wide range of scholars because of some of its advantages, such as, its novel ideas, potential high compression ratio, the unrelated relations between decoded image and resolution ratio, etc. Though the fractal image coding has a good visual effect, the inherent encoding is quite time-consuming under the circumstance of no others' intervention, which disparately limits its development. According to this problem, the thesis studies deeply the fast algorithm of fractal image coding. And it also studies a lot about how to reduce the coding time at the same time of guaranteeing the quality of the decoded image. The main research contents can be summarized as follows.(1) Analyzing the coding algorithm of the non-research fast fractal image. According to the matching relationship of the range and the definition of domain, the thesis comes up with the improving quad-tree segmentation algorithm, integrating the non-search fast fractal image coding algorithm into the quad-tree segmentation coding algorithm. It also analyzes the relationship among the pixels in the image blocks, defines the differential analysis and proposes the D-R matching criteria, which only search those definition of domains complying with the matching criteria of differential analysis, so that the complexity of the searching process will be reduced. So the fractal image decoding algorithm combining the differential analysis and quad-tree is proposed. In the algorithm proposed in this thesis, the speed is increased by 5.87 times and 7.84 times respectively compared with the the variance algorithm and quad-tree algorithm. And then the peak of signal-to-noise of the decoding image is essentially the same.(2) Studying the wavelet and fractal image coding. Based on the fractal predictive image algorithm enhances the PSNR by 4dB than the fractal image compression algorithm of no-search, satisfied the demand of human vision, and accelerates the coding speed by 10 coding algorithm of the wavelet coefficients'zero-tree structure, the thesis makes full use of differences of the wavelet coefficients in the different layers to apply the D-R matching criteria into it. For fully considering the characteristics of the wavelet coefficients, it handles the wavelet coefficients in the form of absolute value, to avoid the errors caused by simple calculation. Meantime, it also applies the zero-tree coding into the wavelet coefficients whose absolute value is small enough. And it comes up with the improving algorithm of fractal predictive image compressing algorithm based on the wavelet coefficients' zero-tree structure. The simulation experiments show that, the improved algorithm increases nearly 19 times in encoding speed compared with the original algorithm. And then the peak of signal-to-noise ratio and compression ratio of the decoding images are also improved.(3) The thesis proposes a new feature method of reducing the fractal encoding time----ortho difference sum, through searching the best matching principle of the matching blocks for conversion. It also elaborates the definition of the ortho difference sum and proves that the relationship between minimum mean-square error and ortho difference sum. Meanwhile, it fully analyzes the the effects of range block standard deviation and domain block standard deviation on the decoding images, defines the matching search radius and comes up with fast fractal image encoding algorithm based on the ortho difference sum. The simulation results show that, the algorithm proposed by the thesis increases by 3.13 times and 5.52 times respectively in encoding speed compared with cross-trace algorithm and variance algorithm. At the same time, the peak of signal-to-noise ratio and compression ratio of the decoding images are also improved slightly.