Tight frames of compactly supported multivariate multi-wavelets (Q2654211)

A general construction of compactly supported tight frames of multi-wavelets in \(L^2(\mathbb{R}^n)\) is described, which is based on the unitary extension principle. A necessary condition for the existence of tight frame generators is derived which yields a construction of a multiresolution analysis by reducing the factorization task of the associated polyphase matrix-valued Laurent polynomial. Examples are given for multivariate scalar- and vector-valued subdivision schemes. For \(C^1\) and \(C^2\) piecewise cubic schemes a corresponding \texttt{Matlab} code is given in the appendix.