Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets
Hongyun Liu · Shuxue jikan · 2008
The notion of vector-valued multiresolution analysis is introduced and the con- cept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and suffcient condition on the existence of orthogonal vector-valued wavelets is given by means of parauni- tary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L2(R,Cn) from these wavelet packets.