We analyze the internal structure of the multiresolution analyses of L2(Rd) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V0 to be the closed linear span of the shifts of the scaling function and W0 that of the shifts of the wavelets. Finally, define V1 to be the dyadic dilation of V0. We characterize the condi...

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale twoand three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on subdivision. The -subdivision scheme only double...

The paper introduces spline wavelets as a modelling tool for system identification and proposes the technique of consistent output prediction using wavelets for estimating system parameters. It suggests that direct weighted summation of projections in approximation space could be used for deriving consistent output prediction in case model structure is built with spline wavelets. This can be vi...

We provide a simple representation of Strr omberg's wavelets which was studied in Strr omberg'83]. This representation enables us to compute those wavelets eeciently. We point out the multiresolution approximation associated with this wavelet and the connection with Chui-Wang's cardinal spline wavelet. A generalization of Strr omberg's wavelet is also given.

This paper presents a construction of compactly supported dual functions of a given box spline in L2(IR ). In particular, a concrete method for the construction of compactly supported dual functions of bivariate box splines of increasing smoothness is provided. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines, matrix extension

We discuss here wavelets constructed from periodic spline functions. Our approach is based on a new computational technique named Spline Harmonic Analysis (SHA). SHA to be presented is a version of harmonic analysis operating in the spaces of periodic splines of defect 1 with equidistant nodes. Discrete Fourier Transform is a special case of SHA. The continuous Fourier Analysis is the limit cas...

In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian) or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The pa...

This study focuses on identifying damage in reinforced concrete (RC) beams using time-domain modal testing and wavelet analysis. A numerical model of an RC beam was used to generate various scenarios with different severities locations. Acceleration time histories were recorded for both damaged undamaged structures. Two indices, DI_MW DI_SW, derived from the analysis, employed determine locatio...

Abstract: The idea of summing pairs of so-called semi-wavelets has been found to be very useful for constructing piecewise linear wavelets over refinements of arbitrary triangulations. In this paper we demonstrate the versatility of the semi-wavelet approach by using it to construct bases for the piecewise linear wavelet spaces induced by uniform refinements of four-directional box-spline grids.

The objective of this paper is to introduce a general scheme for the construction of interpolatory approximation formulas and compactly supported wavelets by using spline functions with arbitrary (nonuniform) knots. Both construction procedures are based on certain “optimally local” interpolatory fundamental spline functions which are not required to possess any approximation property.