Nontensor Product Wavelet Packets in $L_2 (\mathbb{R}^s )$

Abstract

Coifman and Meyer constructed univariate and tensor product bivariate orthonormal wavelet packets in [Orthonormal wave packet bases, preprint]. In this note, we give a general way to construct nontensor product orthonormal multivariate wavelet packets with an exponential decay. In particular, we give concrete constructions of exponentially decaying orthonormal wavelet packets and compactly supported semiorthogonal wavelet packets of two and three variables directly from the scaling function and its refinement mask.