Construction of uniformly symmetric bi-frames based on multiresolution template algorithm

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.

KEYWORDS:

• Bi-frames
• templates
• decomposition and reconstruction algorithm
• uniform symmetry
• parameterization
• curve multiresolution processing

2000 AMS SUBJECT CLASSIFICATIONS:

• 42C40
• 65T60
• 68U07
• 65D17

Acknowledgements

The first author is also very grateful to the Mathematics Department of Georgia Institute of Technology for providing her very good office environment.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors appreciate the support of the National Natural Science Foundation of China [Grant No. 61272028] and the support of the China Scholarship Council [No. 201406885047].