The Basic Theory Of The Second Generation Wavelet And Its Application In The Image Compression

At present, the application of wavelet analysis is a wide use in nature science, application science and economic fields, the lifting scheme is a research hotspot with its flexibility, simpleness and other advantage, and researching the basic theory and exploring the application aspect is one of the important problems in mathematic and information science fields.This paper analyses some important theory of traditional wavelet such as multiresolution, the mallat algorithm and biorthogonal filter sets. Then the lifting scheme using to construct the second generation wavelet is inducted. We compare the first generation wavelet based on the traditional filters with the second generation wavelet based on the lifting scheme, give the procedure of realizing the mallat with lifting scheme and the method of constructing the new wavelet by adaptively choosing the lifting coefficient, and analyze the advantage of lifting scheme in arithmetic complexity and constructing.It proves that the improved lifting coefficient can add to the vanishing moment of the wavelet function in a constructed way, and the adding means to a more centralized energy property. We separatedly use the haar and improved haar in image compression and give the contrast experiment result, which indicates that the latter has a better compression effect. In the end ,the paper discussed the wavelet analysis and its realization in the JPEG2000 codec system. As the kernel of JPEG2000, the wavelet improves the arithmetic efficiency by realizing with lifting scheme. At the other hand, we can replace the wavelet of JPEG2000 with a new wavelet base constructed by the lifting scheme to satisfy a certain application demand.Familiar with the basic theory and understanding the lifting scheme can flexibly analyze the signal. In the signal the image analysis, using the lifting scheme can further some new image compression algorithm to obtain better compression effect.