Construction of uniformly symmetric bi-frames based on multiresolution template algorithm. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Cui, Lihong; Li, Xuguang; Sun, Jianjun
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 6(2019)
• Page Start: 1192
• Page End: 1216
• Publication Date: 2019-06-03
• Subjects: Bi-frames -- templates -- decomposition and reconstruction algorithm -- uniform symmetry -- parameterization -- curve multiresolution processing; 42C40 -- 65T60 -- 68U07 -- 65D17; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1447664
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we focus on the construction of wavelet bi-frames with three generators and uniform symmetry which play an important role in the applications for curve multiresolution processing. We first establish some templates of the decomposition and reconstruction algorithm corresponding to wavelet bi-framelet by several iterative steps. These templates allow parameterization of wavelet bi-framelet filter banks with three symmetric generators. Then the parameters in the filter can be determined by solving systems of nonlinear equations related to the sum rules for the refinement mask and the vanishing moments of framelets, which led to the wavelet bi-frames with desired properties. Some examples of uniform symmetry bi-frames with three generators are presented to illustrate efficient of our methods.