Hermite multiwavelets for manifold-valued data

TL;DR

This paper introduces a method for constructing interpolatory Hermite multiwavelets tailored for functions valued in nonlinear geometries like Riemannian manifolds and Lie groups, extending wavelet theory to manifold-valued data.

Contribution

It develops a prediction-correction approach based on Hermite subdivision schemes for manifold-valued data, demonstrating comparable wavelet coefficient decay to linear Hermite wavelets.

Findings

Wavelet coefficients decay similarly to linear Hermite wavelets

Extension of wavelet theory to manifold-valued functions

Generalization of scalar wavelet results to nonlinear geometries

Abstract

In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. We rely on the strong connection between wavelets and subdivision schemes to define a prediction-correction approach based on Hermite subdivision schemes that operate on manifold-valued data. The main result concerns the decay of the wavelet coefficients: We show that our manifold-valued construction essentially admits the same coefficient decay as linear Hermite wavelets, which also generalizes results on manifold-valued scalar wavelets.