Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of M = ( 1 1 1 −1 )-wavelets is obtained.

The fundamental ideas of wavelets are introduced within the context of mathematical physics. We present essential background notions of mathematical bases, and discuss Fourier, polynomial, and wavelets bases in this light. We construct several types of wavelets and wavelet-like bases and illustrate their use in algorithms for the solution of a variety of integral and di erential equations.

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.

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...