Application Of Wavelet Transform In Static Image Compression

As one important technology of image processing, image compression has many methods at present. But how to find a better method to gain better compression results also is an important research field. Wavelet transform in image compression is one of the hot points in image compression field.In this paper, the foundation theory, classification and the quality evaluation standard of image compression are introduced briefly first. The theoretic foundation of wavelet transform, which include continuous wavelet transform, Multi-resolution analysis, Mallat algorithm, double orthogonal wavelet transform are researched by the view of mathematic. From the analysis of the characteristics of the image coefficient distribution and gradation histogram, which are obtained after the wavelet transform, this paper obtains the important bases of image compression: the majority of image data and the energy concentrate in the low-frequency coefficient, and the majority of high-frequency coefficients distribute nearby zero, and their gradation histograms are similar, the high-frequency coefficients may deal with the identical threshold. Several important factors, the selection of wavelet, the filters'length, the level of the transform, how to deal with the boundary, are summarized, and the influence which factors reduce to the image compression through experiments are also analyzed.When applied wavelet transform on image compression, how to select the suitable wavelet for a specific image is an urgent problem, as there are many types of wavelet in different properties. This paper analyzes some import properties of wavelet, including orthogonal, compact support, regularity, symmetry, number of vanishing, and these properties'impact on compression result. Based on these properties the wavelet, this paper designs perfect reconstruction multi-rate wavelet filter banks through Lagrange halfband filters. The wavelet function applying this method can be used to gain a wavelet which matching to the assigns image through the principle of wavelet matching. The method to decide wavelet scale function in accordance with its relevant coefficient of wavelet matching, maximizing the projection coefficient of its subspace, and finally obtaining the best wavelet filter, which is able to be directly applied in image decomposition and reconstruction and gain best compression results. The final superior filter will be used in image compression. The results from the other commonly used filters have been simulated and compared. The subsequent results show that the filters designed through by this article's method can achieve perfect compression results.Reviewing the research of image coding based on wavelet transmission and update wavelet image coding, systematically reiterating EZW(Embedded Zerotree Wavelets Encoding) and SPIHT(Set Partitioning In Hierarchical Trees) image compression arithmetic of wavelet with detailed analysis of their principle and implementation procedure. And the two image coding arithmetic has carried on the realization and compared.