the vanishing moments property) plays a crucial role in In particular, the orthogonality of the wavelets to the polynomials up to a Of using some of them in simple circumstances. In particular in we study some properties of the wavelet bases considered and the advantages The results reported here and in extend thoseĪnd aim to show not only the theoretical relevance of these wavelet basesīut also their effective applicability in real problems. Made of piecewise constant functions (see,įor example, ), and are a simple variation of the multi-wavelets bases introduced by Alpert in. The wavelet bases introduced generalize the classical Haar's basis, that has only one vanishing moment and is The numerical results shown in Section 4 and in Ĭorroborate these statements both from the qualitative and the quantitative Thanks to these properties these wavelet bases in severalĪpplications can outperform in actual computations the classical wavelet basesĪnd, for example, in we show that they have very good approximation andĬompression properties. Studied in, in general, make use of more than one wavelet motherįunction.
Where the discontinuities occur when, for example, continuous functions areĪpproximated with discontinuous functions. However the lack of regularity of the piecewise polynomial functions used can This fact makes possible to perform very efficiently some of the mostĬommon computations, such as, for example, differentiation and integration. The mainįeature of these wavelet bases is that they are made of piecewise polynomialįunctions of compact support moreover the polynomials used are of low degreeĪnd generate bases with an arbitrarily high assigned number of vanishing This website we restrict our attention to the case A=(0,1). a parallelepiped in theĮxamples considered), starting from the notion of multiresolutionĪnalysis, we construct wavelet bases of with an (arbitrary) assigned number of vanishing moments. when A is a sufficiently simple set (i.e. Of the square integrable (with respect to Lebesgue measure) real functions defined on A. ,, ) with the introduction of multiresolution analysis and of the fast wavelet transform, and by Daubechies (see ) with the introduction of orthonormal bases of compactly supported wavelets.Įuclidean space and let be the Hilbert space Mathematical analysis and signal processing approaches to the study of wavelets Processing and in many other application fields. Techniques have generated much interest, both in mathematical analysis as well as in signal In the last few decades wavelets and wavelets The support and sponsorship of CASPUR are The numerical experience reported in this website and in the paperĬomputing resources of CASPUR (Roma, Italy) under grant: “ Algoritmi di alte prestazioni
Wavelet mother functions of the wavelet bases used to produce the numerical
#DAUBECHIES WAVELET MATLAB CODE SOFTWARE#
Material and animations that help the understanding of the paper and makesĪvailable to the interested users some software programs that generate the In these applicationĪreas the use of the wavelet bases presented gives very satisfactory results. Kernel sparsification and digital image compression and reconstruction. We focus on two relevant applications: integral We study some of the properties of these wavelet bases in particular weĬonsider their use in the approximation of functions and in numerical quadrature. (low degree) polynomial functions with an (arbitrary) assigned number of We present wavelet bases made of piecewise Integral kernel sparsification, image compression and Math codes that compute the wavelet mother functions of the wavelet bases used Serrani”, Università Politecnicaĭelle Marche, Piazza Martelli 8, 60121 Ancona, Italy.Ĭastelnuovo”, Università di Roma “La Sapienza”, Wavelet bases made of piecewise polynomial functions: approximation theory, quadrature rules and applications to integral kernel sparsificationĮ Informatica, Università di Camerino, Via Madonna delle Carceri 9, 62032