Research On Still Image Coding Based On Wavelet Transform

Wavelet theory has been a topic of research in application math and engineering science. It is an important breakthrough of mathematics after Fourier transform. Wavelet transform and Fourier transform are both linear transforms, but Wavelet transform has the double localized property at time-plane and frequent-plane, so it is more flexible than Fourier transform and is profitable to the time-frequent characteristic of the signal. In 1989, Mallat brings forward the idea of Multi-Resolution Analysis and unites the constructed way of all the Wavelet functions, so Wavelet transform is applied widely in image compression. Compared with traditional image coder, the Wavelet image coder can compress image effectively and produce easily the embedded bit stream. This paper researchs the math theory base of Wavelet transform and the character of the Wavelet transform applied on image compressions, and it develops the different correlation of wavelet coefficients by Zerotree conception and suggests two significative embedded image coding by means of some characters of wavelet coefficients on the base of EZW and SPIHT. The main innovative work of this dissertation is summarized as follows: Firstly, continuous and discrete wavelet transform is researched according to analysis of the shortcoming of Short Time Fourier Transform. Mallat algorithm is deduced from the viewpoint of Multi-Resolution Analysis, and filter banks is used to construct orthogonal and biorthogonal wavelet basis.Secondly, Wavelet basis is selected according to the requirements of image compression. Finite support signal is transformed by wavelet basis in order to reconstruct image as possible as alike. Lots of experiments show the distribution character and the degree of correlation of sign, within-subband and cross-subband of wavelet coefficients and provide transcendental knowledge for later coding.Next, according to the detailed sdudy of EZW, the paper points out the shortcomings of the algorithm. On the base of EZW, the EZW algorithm is brought forward. The algorithm improves the compression performance through the nether ways: because the LL subband occupies the great energy of transfonn coefficient, it codes solely the LL subband by predictive coding based on the grads of neighbor coefficient. Here, the paper brings forward separate coding to the extent and the sign of predictive errors, the extent of errors is coded by arithmetic coding according to the bit plane, the sign of errors is coded to remove the redundance of signs by the model of context-based sign coding; For the high-frequent...