Research Of Adaptive Wavelet Transform Based On Lifting Scheme

Wavelet analysis has attracted many researchers'attentions in recent twenty years. It becomes one of the important tools in harmonic analysis and signal analysis fields. Being as the second generation wavelet with the special algorithm structure, the lifting wavelet is proposed for improving the operation speed of traditional wavelet and reducing the memory requirement. It is also fit for adaptive,nonlinear,non oddity sampling and integer to integer transform, so it becomes a research hotspot in the information science field.In the traditional wavelet transform, because the wavelet filter and coefficient is fixed, as a result, when the discontinuous signal is analyzed, it will produce a lot of big wavelet coefficients in the transition, which makes against the compression. In the image processing, some image is roughness, and it may has sharp edges and oddity parts. When we use traditional wavelet analyzing this image, the processing effect is very bad. To solve this problem, we have studied the theory of adaptive wavelet transform via lifting and the application in the image compression.This paper first analyses some basic theory of traditional wavelet such as multiresolution, the Mallat algorithm and biorthogonal filter sets. Then through analyzing the shortcomings of the traditional wavelet, the lifting scheme using to construct the second generation wavelet is inducted. We give the algorithm of getting the coefficients of new lifting wavelet and the procedure of realizing the Mallat with lifting scheme, and introduce the integer lifting scheme wavelet used to the lossless compression. Through analyzing the shortcomings of the liner filter, the adaptive wavelet based on lifting scheme is induced and studied.A new framework for constructing an adaptive wavelet transform via lifting, dual adaptive wavelet transform is proposed in this paper. Both the update and prediction function can shape itself according to the data that it analyses. This gives rise to holding the edge's definition and small wavelet coefficients. For example, it is assumed that update filter utilizes local gradient information to adapt itself to the signal in the sense that smaller gradients"evoke"stronger update filters. As a result, the breaks of the signal won't become blurring, and it...