Multivariate tight wavelet frames with few generators and high vanishing moments

Author:

Hur Youngmi1,Lubberts Zachary2ORCID,Okoudjou Kasso A.3

Affiliation:

1. Department of Mathematics, Yonsei University, Seoul 03722, Korea

2. Department of Applied Mathematics and Statistics, Johns Hopkins University, 3100 Wyman Park Dr, Baltimore, MD 21211, USA

3. Department of Mathematics, Tufts University, Medford, MA 02131, USA

Abstract

Tight wavelet frames (TWFs) are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further develop existing work combining sums of squares representations with TWF construction, and present a new and general method for constructing such frames. Focusing on the case of box splines, we also demonstrate how the flexibility of our approach can lead to TWFs with high numbers of vanishing moments for all of the wavelet masks, while still having few highpass masks: in fact, we match the best known upper bound on the number of highpass masks for general box spline TWF constructions, while typically achieving much better vanishing moments for all of the wavelet masks, proving a nontrivial lower bound on this quantity.

Funder

national research foundation of korea

simons foundation

u.s. army research office

national science foundation

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Information Systems,Signal Processing

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Interpolatory quincunx quasi-tight and tight framelets;Annals of Functional Analysis;2024-09-06

2. Approximation by frame-like multiwavelets;Analysis and Applications;2024-02-29

3. The autoregressive filter problem for multivariable degree one symmetric polynomials;Acta Scientiarum Mathematicarum;2023-03-03

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