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...

The theory of [RS2] is applied to yield compactly supported tight affine frames (wavelets) in L2(IR ) from box splines. The wavelets obtained are smooth piecewisepolynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of “mother wavelets”, however, increases with the increase of the required smoothness. Two bivariate constr...

We construct orthonormal wavelet bases of L2(IR) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H2 of all two-dimensional (2D) scaling coefficients satisfying the orthogonality condition as an implicit function. This set includes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H2 at HN , the scaling coefficients...

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l (1) regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the tempo...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...