We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.

How are body representations updated when we perform joint rhythmic actions, such as when a jazz player synchronizes with other musicians in the ensemble? We investigated this question using a continuous tapping task where musicians and non-musicians were instructed to imitate bimanual hand movements presented in the egocentric and the mirror orientation. The observed movements increased in tem...

In this paper, we give an algorithm to construct semi-orthogonal symmetric and anti-symmetric M-band wavelets. As an application, some semi-orthogonal symmetric and anti-symmetric M-band spline wavelets are constructed explicitly. Also we show that if we want to construct symmetric or anti-symmetric M-band wavelets from a multiresolution, then that multiresolution has a symmetric scaling function.

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

2 Garofalakis & Gibbons, VLDB 2001 # Outline • Intro & Approximate Query Answering Overview – Synopses, System architecture, Commercial offerings • One-Dimensional Synopses – Histograms, Samples, Wavelets • Multi-Dimensional Synopses and Joins – Multi-D Histograms, Join synopses, Wavelets • Set-Valued Queries – Using Histograms, Samples, Wavelets • Advanced Techniques & Future Directions – Stre...

We demonstrate that many multivariate wavelets are projectable wavelets; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tensor product (nonseparable) wavelets. We show that a projectable wavelet can be replaced by a tensor product wavelet without loss of desirable properties such as spatial localization, smoothness and vanishing moments.

We construct piecewise constant wavelets on spherical triangulations, which are orthogonal with respect to a scalar product on L(S), defined in [3]. Our classes of wavelets include the wavelets obtained by Bonneau in [1] and by Nielson et all. in [2]. We also proved the Riesz stability and showed some numerical experiments.

In this paper, we present comparative analysis of scale-invariant feature extraction using different wavelet bases. The main advantage of the wavelet transform is the multi-resolution analysis. Furthermore, wavelets enable localization in both space and frequency domains and high-frequency salient feature detection. Wavelet transforms can use various basis functions. This research aims at compa...

In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in a later stage. We show how lifting leads to a faster, fully in-place implementation of the wavel...

Construction of higher multiplicity wavelets adapted to a particular task is discussed. The proposed method uses parameterization of wavelet matrices. Large classes of wavelet matrices are searched to minimize a given cost function on training data. The method is applied to a problem of detecting and possibly removing a disturbance of a certain kind from a signal. The importance of choosing the...