Related papers: Wavelet Sets and Generalized Scaling Sets on Vilen…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Finding efficient representations is one of the most challenging and heavily sought problems in mathematics. Representation using shearlets recently receives a lot of attention due to their desirable properties in both theory and…
This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
We construct the spectrum for a shift invariant space on Vilenkin group. We prove the results related to spectrum and Frame multiresolution analysis for Cantor dyadic group and Vilenkin group.
In this article, we follow closely the approach in Hernandez and Weiss's seminal text in describing the construction of an orthonormal wavelet from a multi-resolution analysis. We assume the reader has a modest background in analysis and…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the…
We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes.…
We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby…
A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace…
We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on $\mathbb R^n$ with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations…
We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…
A multiresolution analysis associated with linear canonical transform was defined by Shah and Waseem for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…
A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in $L^2(\mathbb R)$. This example has the same multiplicity function as the Journ\'e wavelet, yet has a $C^{\infty}$…
On a compact interval, we introduce and study a whole family of wavelets depending on a free parameter that can be suitably modulated to improve performance. Such wavelets arise from de la Vall\'ee Poussin (VP) interpolation at Chebyshev…