This paper deals with the construction of biorthogonal p -wavelet packets on R+ related to the Walsh polynomials and their properties are investigated by means of Walsh-Fourier transform. Three biorthogonal formulas regarding these p -wavelet packets are derived. Moreover, it is shown how to obtain several new Riesz bases of the space L2(R+) by constructing a series of subspaces of these p -wav...

Multispectral geospatial image sets retain the scene’s spatial and spectral information. To jointly use both of them for analysis purposes, we propose to extend the concept of wavelet packets, by introducing a new integrated multispectral entropy function. Each spectral band is individually decomposed by the wavelet packets transform, and then the entropy term is jointly guided by information f...

This paper introduces Group Testing for Wavelet Packets (GTWP), a novel embedded image compression algorithm based on wavelet packets and group testing. This algorithm extends the Group Testing for Wavelets (GTW) algorithm [7] to handle wavelet packets. Like its predecessor, GTWP obtains good compression performance without the use of arithmetic coding. It also shows that the group testing meth...

We study the mean size of wavelet packets in Lp. An exact formula for the mean size is given in terms of the p-norm joint spectral radius. This will be a corollary of an asymptotic formula for the Lp-norms on the subdivision trees. Then the stability and Schauder basis property of wavelet packets in Lp, and the instability of biorthogonal wavelet packets in L2 are analyzed. AMS Subject Classifi...

Speech process has benefited a great deal from the wavelet transforms. Wavelet packets decompose signals in to broader components using linear spectral bisecting. In this paper, mixtures of speech signals are decomposed using wavelet packets, the phase difference between the two mixtures are investigated in wavelet domain. A geometrical model is defined and an adaptive algorithm is proposed bas...

To use wavelet packets for lossy data compression, the following issues must be addressed: quantization of the wavelet subbands, allocation of bits to each subband, and best-basis selection. We present an algorithm for wavelet packets that systematically identifies all bit allocations/best-basis selections on the lower convex hull of the rate-distortion curve. We demonstrate the algorithm on tr...

This correspondence investigates M -band wavelet packets and a generalized framework for the design and efficient utilization of multirate filter bank trees (FBTs). While the increased flexibility of M -band wavelet packets over the standard 2-band wavelet packets is desirable in many signal processing applications, the possibilities in time-frequency design using arbitrary filter bank cascades...

The anisotropic wavelet packet transform is an extension of the conventional wavelet (packet) transform where the basis can have di erent scales in di erent dimensions. As there are certain kinds of images with di erent behaviour in horizontal and vertical direction, anisotropic wavelet packet bases can be adapted more precisely to these images. Zero-tree image compression has already proved it...

We show that asymptotic estimates for the growth in L(R)-norm of a certain subsequence of the basic wavelet packets associated with a finite filter can be obtained in terms of the spectral radius of a subdivision operator associated with the filter. We obtain lower bounds for this growth for p 2 using finite dimensional methods. We apply the method to get estimates for the wavelet packets assoc...