Related papers: A directional continuous wavelet transform on the …
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
We establish a necessary and sufficient condition on a continuous function on $[-1,1]$ under which the family of functions on the unit sphere $\mathbb{S}^{d-1}$ constructed in the described manner is fundamental in $C(\mathbb{S}^{d-1})$. In…
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…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
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…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
We introduce a new class of autoregressive models for spherical time series, where the dimension of the spheres on which the observations of the time series are situated may be finite-dimensional or infinite-dimensional as in the case of a…
A new integration method drastically improves the efficiency of the dark matter direct detection calculation. In this work I introduce a complete, orthogonal basis of spherical wavelet-harmonic functions, designed for the new vector space…
We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
We present a new spectral scheme for analysing functions of half-integer spin-weight on the $2$-sphere and demonstrate the stability and convergence properties of our implementation. The dynamical evolution of the Dirac equation on a…
Waveguide design is crucial in developing efficient light delivery systems, requiring meticulous material selection, precise manufacturing, and rigorous performance optimization, including dispersion engineering. Here, we introduce…
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…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…
We describe a new method involving wavelet transforms for deriving the wind velocity associated with atmospheric turbulence layers from Generalized SCIDAR measurements. The algorithm analyses the cross-correlation of a series of…