Construction for a class of smooth wavelet tight frames  

作　　者：彭立中 王海辉 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science in China(Series F)》2003年第6期445-458,共14页中国科学（F辑英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.90104004 and 69735020);973 Project of China(Grant No.G1999075105).

摘　　要：From the inequality |P(z)|2 + |P(-z)|2 ≤1, assuming that both of the low-pass filters and high-pass filters are unknown, we design compactly supported wavelet tight frames. The unknowing of low-pass filters allows the design more freedom, and both the low-pass filters and high-pass filters have symmetries or anti-symmetries. We give the algorithm for filters with odd and even lengths separately, some concrete examples of wavelet tight frames with the length 4, 5, 6, 7, and at last we give the result of decomposing Lena image with them.From the inequality |P(z)|2 + |P(-z)|2 ≤1, assuming that both of the low-pass filters and high-pass filters are unknown, we design compactly supported wavelet tight frames. The unknowing of low-pass filters allows the design more freedom, and both the low-pass filters and high-pass filters have symmetries or anti-symmetries. We give the algorithm for filters with odd and even lengths separately, some concrete examples of wavelet tight frames with the length 4, 5, 6, 7, and at last we give the result of decomposing Lena image with them.

关 键 词：wavelet tight frame compact support SMOOTHNESS symmetry (anti-symmetry). 

分 类 号：TN713[电子电信—电路与系统]