Interpolatory tight wavelet frames with prime dilation

Youngmi Hur, Zachary Lubberts

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the prime coset sum method for constructing tight wavelet frames, which allows one to construct nonseparable multivariate tight wavelet frames with prime dilation, using a univariate lowpass mask with this same prime dilation as input. This method relies on the idea of finding a sum of hermitian squares representation for a nonnegative trigonometric polynomial related to the sub-QMF condition for the lowpass mask. We prove the existence of these representations under some conditions on the input lowpass mask, utilizing the special structure of the recently introduced prime coset sum method, which is used to generate the lowpass masks in our construction. We also prove guarantees on the vanishing moments of the wavelets arising from this method, some of which hold more generally.

Original languageEnglish
Pages (from-to)897-915
Number of pages19
JournalApplied and Computational Harmonic Analysis
Volume49
Issue number3
DOIs
Publication statusPublished - 2020 Nov

Bibliographical note

Funding Information:
This research was supported in part by the National Research Foundation of Korea (NRF) [Grant Number 20151009350].

Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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