This article obtains the nonseparable version of wavelet packets on ~a and generalizes the "'unstability" result of nonorthogonal wavelet packets in Cohen-Daubechies to higher dimensional cases. 1 . I n t r o d u c t i o n The wavelet packets introduced by R. Coifman, Y. Meyer, and M. V. Wickerhauser played an important role in the applications of wavelet analysis as shown, for example, in [CMW...

In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is deened. A corresponding shift-invariant wavelet packet decomposition (SIWPD) search algorithm for a \best basis" is introduced. The search algorithm is representable by a binary tree, in which a node symbolizes an appropriate subspace of the original signal. We prove that the resultant...

Parameterized wavelet filters and wavelet packet subband structures are discussed to be used as key dependent wavelet transforms in order to enhance the security of wavelet based hashing schemes. Experiments show that key dependency and keyspace of the hashing scheme considered have been significantly improved. The attack resistance could only be slightly enhanced by using parametrized wavelet ...

We consider best m-term approximation in Lp(R) with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) for a large class of wave packets are completely characterize...

The continuous wavelet transform is employed to analyze the dynamics and time-dependent energy distribution of phonon wave-packet propagation and scattering in molecular dynamics simulations. The equations of the one-dimensional continuous wavelet transform are presented and then discretized for implementation. Practical aspects and limitations of the transform are discussed, with attention to ...

We present a technique for lossy image compression based on the joint-adaptive space and frequency decomposition of images. The algorithm adapts to image content by both developing wavelet packet bases for separate areas of the image and by segmenting image subbands as needed. The elements of the expansion are a two-channel lter bank and a complete and disjoint binary segmentation system. We co...

This article compares results obtained in previous studies using time-frequency representations (Wigner-Ville, Choi-Williams and Parametric) and the wavelet transform with those obtained with wavelet packet functions to show new findings about their quality in the analysis of ECoG recordings in human intractable epilepsy: data from 21 patients have been analyzed and processed with four types of...

Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in co...