The Construction Of Biorthogonal Multiwavelet Packets And The Design Of Prefilter

Wavelets are a useful tool for signal processing applications such as image compression and denosing. But there is not such a signal wavelets that possess compact-support, orthogonality, and symmetry at the same time. Multiwavelet theory is the new development of wavelet theory. Multiwavelet can satisfy orthogonality, symmetry, compact support and high-vanish moment at the same time. So it has better properties than those of traditional wavelet.In this paper, we firstly summarize the multiwavelet theory and wavelet packets theory.As the supplementary to the multiwavelet theory, a method for construction of biorthogonal multiwavelet packets with multi-scale is proposed in the paper. By introducing the concept of wavelet packets into biorthogonal multiwavelet packets, the multi-scaling biorthogonal multiwavelet packets is constructed, and the properties corresponding to the traditional wavelet packets are proved. Concrete works as follows:(1) the concept of biorthogonal multiwavelet packets is established;(2) the Fourier transform of functions in biorthogonal multiwavelet packets is obtained;(3) biorthogonal relation of two families of functions in biorthogonal multiwavelet packets is proved;(4)by constructing biorthogonal multiwavelet packets,we get two bases of L~2(r) which satisfied biorthogonal relation.Owing to the ways of relaxed construction in biorthogonal case, the method proposed here has comparatively larger values in application.Preprocessing is an unavoided process in application of multiwavelets. The paper also does some works in designing of prefilter:(1) this paper gets a new project of adaptive multiwavelet prefilter; (2)give examples to proof the feasibility of this project.