Related papers: Wavelet Sets and Generalized Scaling Sets on Vilen…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
For a given symmetric refinable mask obeying the sum rule of order $n$, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order $n$. A transformation based on…
The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition…
The local trace function introduced in \cite{Dut} is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of…
We consider a class of semidirect products $G = \mathbb{R}^n \rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
We propose a new multiscale method to calculate the amplitude of the gradient of the linear polarisation vector using a wavelet-based formalism. We demonstrate this method using a field of the Canadian Galactic Plane Survey (CGPS) and show…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
The generalized quantum group of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra, which appears in the study of solutions to the tetrahedron equation or the three-dimensional Yang-Baxter…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
Mesoscale structures can often be described as fractional dimensional across a wide range of scales. We consider a $\gamma$ dimensional measure embedded in an $N$ dimensional space and discuss how to determine its dimension, both in $N$…
We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…
Shah and Abdullah [Complex Analysis Operator Theory, 9 (2015), 1589-1608] have introduced a generalized notion of nonuniform multiresolution analysis (NUMRA) on local field $K$ of positive characteristic in which the translation set…
In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
We collect some new results relative to the study of the spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness.