Wavelet packets have been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal nonseparable five-variantl wavelet packets is introduced. A new approach for de-signing them is presented by iteration method. We proved that the fivevariant wavelet packets are of the orthogonality trait. We give three orthogonality formulas regarding...

The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.

We study wavelet packets in the setting of a multiresolution analysis of L2(Rd) generated by an arbitrary dilation matrix A satisfying |det A| = 2. In particular, we consider the wavelet packets associated with a multiresolution analysis with a scaling function given by the characteristic function of some set (called a tile) in Rd. The functions in this class of wavelet packets are called gener...

Sherman D. Riemenschneider Zuowei Shen Department of Mathematics Department of Mathematics West Virginia University National University of Singapore Morgantown, WV 26506 Singapore 119260 [email protected] Abstract: In this note, we present a construction of interpolatory wavelet packets. Interpolatory wavelet packets provide a ner decomposition of the 2jth dilate cardinal interpolation spa...

In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.

Diffusion wavelets can be constructed on manifolds, graphs and allow an efficient multiscale representation of powers of the diffusion operator that generates them. In many applications it is necessary to have time–frequency bases that are more versatile than wavelets, for example for the analysis, denoising and compression of a signal. In the Euclidean setting, wavelet packets have been very s...

In this paper, we introduce the notion of biorthogonal wavelet packets associated with nonuniform multiresoltion analysis and study their characteristics by means of Fourier transform. Three biorthogonal formulas regarding these wavelet packets are established. Moreover, it is shown how to obtain several new Riesz bases of the space (R) by constructing a series of subspaces of these nonuniform ...