True 2-D Lifting Wavelet Design And Its Application In Data Compression

The image encoding, 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 & video encoding fields for its special capability of Multi-Resolution Analysis. Wavelet encoding is a new and vital development direction in transform encoding. With the proclamation of JEPG2000 standard, wavelet encoding will be the mainstream technology in image & video encoding fields.In this paper, true 2-D wavelet transform and its lifting scheme and Binary Tree wavelet encoding & decoding algorithm to Image Compression which is suitable for this wavelet are mainly studied. First of all, 1-D wavelet transform, Multi-Resolution Analysis and orthogonal wavelet decomposition & reconstruction algorithm are briefly introduced. Secondly, the separable 2-D wavelet transform, its decomposition & reconstruction algorithm, and lifting scheme are discussed. With the basic idea of wavelet transform image encoding, SPIHT encoding algorithm is introduced.In the following, the sampling of 2-D discrete signal is discussed, and All Phase Interpolating Filter Banks are designed based on the theory of All Phase Sequency Filting. Using the All Phase Interpolating Filter Bank as the prediction and update filter in wavelet lifting scheme, the realization of the true 2-D wavelet transform with lifting scheme is introduced in detail. After the true 2-D wavelet transform, considering the characteristics of wavelet coefficients in all decomposition sub-bands and the basic idea of classical SPIHT wavelet encoding algorithm, Binary Tree Wavelet encoding & decoding algorithms are proposed with detailed instance.Finally, the true 2-D wavelet transform of images with lifting scheme, binary tree encoding algorithm and are realized with Matlab program. 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 encoding algorithm SPIHT at low bit rates.