Related papers: On alternative wavelet reconstruction formula: a c…
The main result of our paper offers an alternative, simpler, proof of Mallat's result on the translation invariance of the limiting behavior of sequences of Wavelet Scattering Transforms, which (unlike Mallat's proof) does not rely on the…
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
In this work, we extend the x-ray constrained wavefunction fitting approach, a key method in quantum crystallography for charge density reconstruction, to incorporate experimental observables beyond x-ray diffraction. Unlike traditional…
Detections of gravitational-wave signals from compact binary coalescences have enabled us to study extreme astrophysical phenomena and explore fundamental physics. A crucial requisite for these studies is to have accurate signal models with…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
A new set of symmetric correction functions is presented for high-order flux reconstruction, that expands upon, while incorporating, all previous correction function sets and opens the possibility for improved performance. By considering FR…
High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic…
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness.…
The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial…
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…
It is challenging for full-waveform inversion to determine geologically informative models from field data. An inaccurate wavelet can make it more complicated. We develop a novel misfit function, entitled deconvolutional double-difference…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
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…