The image coding, which is a significant branch of Digital Image Processing, is extensively applied in various transmitting, storage and retrieval systems of image & video. Since 1980s, the wavelet transform has been well applied in image and video coding for its special capability of Multi-Resolution Analysis. Wavelet coding is a new and vital development direction in transform coding. With the proclamation of JPEG2000 standard, wavelet coding will be the mainstream technology in image & video coding fields.In this paper, Binary Tree wavelet encoding & decoding algorithm to Image Compression is mainly studied based on nonseparable two-dimensional wavelet transform on Lifting Scheme. First of all, one-dimensional wavelet transform, Multi-Resolution Analysis and Mallat algorithm are briefly introduced, and then the boundary extension problem in Mallat algorithm's realization is also discussed, moreover, an illustration of Mallat algorithm is given with periodic extension methods. Secondly, separable two-dimensional wavelet transform and two-dimensional Mallat algorithm are studied. Separable two-dimensional wavelet transform of the image is implemented with C program; and the statistical analysis and energy distributing analysis of the corresponding wavelet coefficients are dealt with using Matlab6.5, thus the characteristic of wavelet coefficients applied to image coding are also analyzed. With the basic idea of wavelet transform image coding, three typical wavelet image coding algorithms are introduced.In the following, the sampling of two-dimensional discrete signal and wavelet lifting scheme are discussed. And All Phase Interpolating Filter Banks is designed based on the theory of the All Phase Sequency Filtering. Using the All Phase Interpolating Filters as the prediction and update filter in wavelet lifting scheme, how to realize the nonseparable two-dimensional wavelet transform with lifting scheme is introduced in detail. Similarly to the separable instance, the image wavelet coefficients, with nonseparable two-dimensional wavelet transform, are processed with statistical analysis. Considering the characteristics of wavelet coefficients in all decomposition subbands and the basic idea of classical SPIHT wavelet coding algorithm, Binary Tree Wavelet Coding Algorithm is proposed with detailed instance.Finally, the nonseparable two-dimensional wavelet transform of images with Lifting Scheme and Binary Tree encoding algorithm are realized with C program in the console of VC6.0. Correspondingly, Binary Tree decoding and wavelet inverse transform are carried out to reconstruct the images. When compressing the classical test images, the results indicate that the compression efficiency is better than the traditional wavelet coding algorithm SPIHT at low bit rates and the Peak Signal-to-Noise Ratio (PSNR) of the reconstructed images are higher than that of SPIHT about 0.4dB. |