Premium
Wavelet bi‐frames with uniform symmetry
Author(s) -
Li Baobin
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3819
Subject(s) - mathematics , wavelet , frame (networking) , symmetry (geometry) , smoothness , algorithm , multiresolution analysis , function (biology) , image (mathematics) , image processing , pure mathematics , wavelet transform , mathematical analysis , artificial intelligence , computer science , geometry , discrete wavelet transform , telecommunications , evolutionary biology , biology
Wavelet bi‐frames with uniform symmetry are discussed in this paper. Every refinable function in the bi‐frame system is symmetric, which is very useful in the image processing and curve and surface multiresolution processing. By the aid of the lifting scheme, bi‐frame multiresolution algorithms can be divided into several iterative steps, and each step can be shown by a symmetric template. The template‐based procedure is established for constructing bi‐frames with uniform symmetry and N > 2 generators. In particular, we take the bi‐frame with three generators as an example to provide a clearer picture of the template‐based procedure for constructing bi‐frames. Three types of bi‐frames with three generators are studied, and some examples with certain smoothness are constructed. These examples include some bi‐frames with interpolating property. Copyright © 2016 John Wiley & Sons, Ltd.