Multiwavelet packets and frame packets of $L^2({\mathbb R}^d)

Abstract

The orthonormal basis generated by a wavelet of $L^2(\mathbb R)$ has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of $L^2({\mathbb R}^d)$ is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases of $L^2({\mathbb R}^d)$ from the multiwavelet packets.