Related papers: Wavelet transform and diffusion equations: applica…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
Asymptotic expansion of the wavelet transform for small values of the dilation parameter a is obtained using asymptotic expansion of the Mellin convolution technique ofWong. Asymptotic expansions of Morlet wavelet transform, Mexican hat…
The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
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 consider imaging of fast moving small objects in space, such as low earth orbit satellites. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
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…
We propose an unsupervised image fusion architecture for multiple application scenarios based on the combination of multi-scale discrete wavelet transform through regional energy and deep learning. To our best knowledge, this is the first…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Reconstructing the early Universe from the evolved present-day Universe is a challenging and computationally demanding problem in modern astrophysics. We devise a novel generative framework, Cosmo3DFlow, designed to address dimensionality…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…