An important tool for the construction of tight wavelet frames is the
Unitary Extension Principle first formulated in the Fourier-domain by
Ron and Shen. We show that the time-domain analogue of this prin-
ciple provides a unified approach to the construction of tight frames
based on many variations of multiresolution analyses, e.g. regular refinements of bounded L-shaped domains, refinements of subdivision
surfaces around irregular vertices, and nonstationary subdivision. We
consider the case of nonnegative refinement coefficients and develop
a fully local construction method for tight frames. Especially, in the
shift-invariant setting, our construction produces the same tight frame generators as the Unitary Extension Principle.
2000 MSC: 42C40 primary, 42C15, 42C30 secondary
Keywords: Wavelet frames, Unitary Extension Principle, irregular MRA,
nonstationary MRA