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

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