Symmetric interpolatory dual wavelet frames

TL;DR

This paper presents a method for constructing symmetric, interpolatory wavelet frames with arbitrary order sum rules, ensuring dual frames with symmetric masks and specified vanishing moments, tailored for various symmetry groups.

Contribution

It provides explicit construction techniques for symmetric refinable masks and dual wavelet frames with desired symmetry and vanishing moment properties for any symmetry group.

Findings

Constructed $H$-symmetric refinable masks with arbitrary sum rule order.

Developed explicit methods for dual wavelet frames with symmetric masks and vanishing moments.

Modified techniques for abelian groups to ensure $H$-symmetry of wavelet masks.

Abstract

For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we give an explicit technique for the construction of dual wavelet frames such that the corresponding wavelet masks are mutually symmetric and have the vanishing moments up to the order n. For an abelian symmetry group $H$ we modify the technique such that each constructed wavelet mask is $H$-symmetric.