Parseval frame multiwavelets associated with A-FMRA

The multiwavelet functions have more desired properties than any single wavelet function, such as short support, symmetry, and smoothness, which provide interesting applications in signal processing and some other fields. In this paper, we study Parseval frame multiwavelets (PFMs) with an arbitrary expanding matrix dilation in higher dimensions. We prove that all PFMs associated to frame multiresolution analysis are equivalent to semi-orthogonal Parseval frame multiwavelets, and characterize all PFMs associated to frame multiresolution analysis by showing that they correspond precisely to those for which the dimension function is non-negative integer-valued. Copyright © 2010 Binary Information Press.