相关论文: Practical wavelet design on the sphere

We show how spatial dispersion can be used as a mechanism to customize the longitudinal profiles of electric fields inside modulated wire media, using a fast and remarkably accurate 1D inhomogeneous model. This customization gives fine…

Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…

We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover…

Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very…

We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…

This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial approximations for functions in these…

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and…

This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…

In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of…

Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays we introduced. In the current paper, we propose the wavelets to analyze such images. The…

We present a new explicit local space-time adaptive framework to decrease the time required for monodomain simulations for cardiac electrophysiology. Based on the localized structure of the steep activation wavefront in solutions to…

A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…

We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…

HEALPix -- the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable…

The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves…

Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…

In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…

The goal of this paper is to study how the symmetry of the spherical domain influences solutions of elliptic equations on such domain. The method pursued is a variant of the moving plane method, discovered by Alexandrov (1962) and used for…

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…

The aim of this paper is to study the nonparametric regression estimators on the sphere built by the needlet block thresholding. The block thresholding procedure proposed here follows the method introduced by Hall, Kerkyacharian and Picard…