Roger L. Claypoole, Jr. and Richard G. Baraniuk, Rice University Summary We introduce and discuss biorthogonal wavelet transforms using the lifting construction. The lifting construction exploits a spatial{domain, prediction{error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We discuss the application of lifting to adaptive and n...

We investigate the formulation of boundary compensated wavelet transforms supported on a nite interval. A uni ed approach to boundary compensated wavelet transforms is presented which fosters new insights into previous constructions, including both continuous and discrete approaches to the problem. The framework enables the design of boundary-compensated transforms with speci c properties, incl...

In geophysical exploration different types of measurements are used to probe the same subsurface region. In this paper we show that the wavelet transform can aid the process of linking different data types. The continuous wavelet transform, and in particular the analysis of amplitudes along wavelet transform modulus maxima lines, is a powerful tool to analyze the characteristic properties of lo...

In paper we describe a successful applications of the wavelet transforms to still image compression. The wavelet transforms were designed by the usage of discrete interpolatory splines. These filters outperform the traditional biorthogonal 9/7 filters which are frequenty used in wavelet based compression. The new filters and the biorthogonal 9/7 are incorporated into SPIHT in order to measure a...

Geometric wavelet-like transforms for univariate and multivariate manifold-valued data can be constructed by means of nonlinear stationary subdivision rules which are intrinsic to the geometry under consideration. We show that in an appropriate vector bundle setting for a general class of interpolatory wavelet transforms, which applies to Riemannian geometry, Lie groups and other geometries, Hö...

In this paper the use of classical and lifting based wavelets for image compression was presented. Both classical and lifting based wavelets are considered. Classical wavelets considered in this work are Haar wavelet, Daubechie wavelet, Coiflet wavelet, Biorthognal wavelet, Demeyer wavelet, and Symlet wavelet. Lifting based wavelet transforms considered are (5,3) and (9,7). Large number of imag...

An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two. The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions. The properties of their autocorrelation functions are studied. The non-periodic complementary sequences are the intersection between anti-symmetric and symme...

This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. As an application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using qwavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

Recent years have seen tremendous increase in the generation, transmission, and storage of color images. A new lossless image compression method for progressive-resolution transmission of color images is carried out in this paper based on spatial and spectral transforms. Reversible wavelet transforms are performed across red, green, and blue color sub bands first. Then adaptive spectral transfo...

We propose a parallel 2D wavelet transform algorithm with modest communication requirements. Data are transmitted between nearest neighbors only and the amount is independent of the problem size as well as the number of processors. An analysis of the theoretical performance shows that our algorithm is highly scalable approaching perfect speedup as the problem size is increased. The algorithm ru...