Wavelet bi-frames with uniform symmetry

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 (C) 2016 John Wiley & Sons, Ltd.