正交四重小波的收敛性与光滑性

Convergence and Smoothness of Orthogonal Maltiplicity Four Mutiwavelets

1996年 ,Chui C K,与 Lian JA在不考虑其收敛性与光滑性的情况下 ,首次得出正交的二重小波 ,引起相当多人的注意。 Jia R Q,Zhou D X等讨论三重小波的收敛性与光滑性 ,给出特例 ,指出Chui与 Lian的二重小波特例的收敛性与光滑性。洪东等讨论了四重小波的特例。本文在此基础上进一步讨论了正交四重小波的收敛性与光滑性 ,给出兼有正交对称 (反对称 )的特例。

Consider the convergence of four orthogonal multiwavelets which refinement equation is in the form φ(x)=∑2k=0h kφ(2x-k) with a 4 vector function φ,4×4 matrices h 0,h 1 and h 2. Then, a basic condition for four orthogonal multiwavelets, some conditions about symmetry or anti symmetry for four orthogonal multiwavelets, constructed methods for four orthogonal symmetry or antisymmetry multiwavelets and an four orthogonal symmetry or antisymmetry multiwavelets are given.