This thesis dedicates itself to the research on still image compression. Image compression is crucial in practical multimedia communication system. At first, the role of image compression in the model of digital communication system is discussed. Information theory is selected as the root for image compression research. Then, several parameters are defined to judge the compression performance. The compression techniques are classified and several international image compression standards are briefly introduced. In chapter 2 we give a brief description of the mathematical theory wavelet analysis on which the paper based, including Fourier transform, Gabor transform, short time Fourier transform, continuos wavelet transform, frame, wavelet progression, multiresolution analysis, fast Mallat algorithm of dyadic wavelet transform, etc. A general transform-based image compression framework is given in chapter 3. To practically apply wavelet theory to decomposition and reconstruction of images, we introduce both 2-dimensional separable and non-separable wavelets. Problems such as orthogonal and biorthogonal wavelets, selection of wavelet bases, image margin extension are all discussed. At the end of the chapter we summarize the wavelet image compression methods since 1980's. We in chapter 4 detailly analyze the spatial-frequencial characteristics of wavelet transformed images. The spatial and frequencial localization capability of wavelet filters and self-similarity of wavelet coefficients across decomposition levels are especially pointed out. Based on above discussion, we thoroughly analyze two excellent zero-tree compression algorithms. The possibility for the integration of these frequencial compression algorithms and spatial compression methods is also explored. Through suppressing high frequency noises and statistically optimizing coefficient reconstruction values the above algorithms are improved. The zero-tree algorithm is used to code and decode grayscale fingerprint images. Excellent results are achieved. Finally, we give a conjecture of the future research directions for still and dynanfic image compression.
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