From full rank subdivision schemes to multichannel wavelets: A constructive approach
This work provides a theoretical framework for constructing matrix wavelets from subdivision schemes, benefiting researchers in signal processing and approximation theory, but the results are incremental.
The paper presents a constructive method to derive multichannel wavelets from full rank vector subdivision schemes, particularly interpolatory ones, enabling efficient generation of orthogonal multiresolution analyses for vector-valued signals. Examples demonstrate the resulting matrix scaling functions and wavelets.
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.