Theory Of Second Generation Wavelet Transforms And Its Application In The Signal And Image Coding Algorithms

In the late 1980s, Daubechies proposed a systematical approach of constructing compactly supported orthogonal wavelet, and Mallat presented multiresolution analysis and discrete wavelet transform.At presently , in the fields of wavelet, the lifting scheme is the key question, not only because of its generality and flexibility ,but also since it allows efficient implementation. Signals and Image information are the important source for human being to explore the world outside and inside, how to use as few coefficients as possible to express the signals and image is the question needed to resolve in a lot of research fields. This paper mainly studied on the theory of wavelet transform based on the lifting schemethe, and proposed the double adaptive wavelet transform based on the lifting scheme for the application in the fields of the signals and image.At the same time, its application in JPEG2000 were researched.Because of its linear peoperties, the biorthogonal wavelet have widely application. To solve for the coefficients of the fast lifting wavelet transform, the new method for calculating the coefficients of the lifting schemes was presented. Because the method proposed here doesn't use the Euclidean algorithm, it is easy to solve the coefficients.Moreover , its results are the same as that obtained by other methods.Lifting scheme is honored as the key tool to construction of second generation wavelets.The paper proposed the new lifting scheme, experiment results demonstrate that the algorithm can acquire the better energy concertration.In the JPEG2000 codec, if it adopted the wavelet transform proposed by the paper, the better image compression quality can obtained.It is well known that the wavelet liner approximation (i.e, truncating the high frequencies ) can be approximate smooth singals very efficiently.However, for example ,piecewise continous signals with large jump in signal value or in its derivatives, standard wavelet linear approximation techniques cannot achieve similar results for signals which are not smooth.To overcome these problems within the standard wavelet transform framework, the paper proposed the double adaptive wavelet transforms. Experiment results show that it can acquire the wavelet linear approximation very efficiently for the smooth and non-smmoth signals.The non-smooth informations have important effects on the image compression, in order to reduce the fluctuated phenomena introduced by the non-smooth informations , the paper presented the double adaptive wavelet transforms based on lifting scheme for image application. Experiment results show that it have better the energy concertration and the image compression quality in JPEG2000 algorithms.The Rate-Distortion Optimization can proposed the flexibility of the JPEG2000 code stream.The new Rate-Distortion Optimization can be presented in this paper, and experiment results show that it can reduced the run time and save on the memory.The scalable wavelet video coding algorithm is the new research aspect, the paper studied on the motion compensated algorithm in the MC-EZBC coding system.