Optimal Biorthogonal Wavelets Base

Discrete hyper-wavelet transforms which is put forward by Guoqiu Wang expand the scope of wavelet transforms, especially for its discrete part. In this paper, we put forward the definition for optimal biorthogonal wavelets base by discrete hyper-wavelet transforms and prove it is true by analyzing the data on image compression. We show the interaction between the optimal condition and the Biorthogonal wavelet filters spectrum.Chapter 1 introduce the wavelet development, Multi Resolution Analysis, the qualities of orthogonal wavelet filters and Biorthogonal wavelet filters. Chapter 2 put forward the definition for optimal biorthogonal wavelets base .Chapter 3 construct some different classes of optimal biorthogonal wavelets filter basing on optimal condition . We prove the definition for optimal biorthogonal wavelets base is reasonable in chapter 4. Chapter 5 show wavelet filters spectrum by discrete hyper-wavelet transforms is bouned . We find it is impossible for any biorthogonal wavelet filters spectrum to infinitely approach to a bounded interval . We find a interval estimation. We also prove that it is impossible for any biorthogonal wavelet transforms to infinitely approach to orthogonal wavelet transforms!...