From full rank subdivision schemes to multichannel wavelets: A constructive approach

TL;DR

This paper explores the development of multichannel wavelets derived from full rank vector subdivision schemes, providing a constructive method and examples for generating orthogonal multiresolution analyses for vector signals.

Contribution

It introduces a constructive approach to derive multichannel wavelets from full rank subdivision schemes, emphasizing efficient construction and practical examples.

Findings

Efficient scheme for constructing multichannel wavelets.

Connection between full rank subdivision schemes and orthogonal multiresolution analysis.

Examples illustrating matrix scaling functions and wavelets.

Abstract

In this paper, we describe some recent results obtained in the context of vector subdivision schemes which possess the so-called full rank property. Such kind of schemes, in particular those which have an interpolatory nature, are connected to matrix refinable functions generating orthogonal multiresolution analyses for the space of vector-valued signals. Corresponding multichannel (matrix) wavelets can be defined and their construction in terms of a very efficient scheme is given. Some examples illustrate the nature of these matrix scaling functions/wavelets.