Needlet approximation for isotropic random fields on the sphere

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

12 Scopus Citations
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Author(s)

  • Quoc T. Le Gia
  • Ian H. Sloan
  • Yu Guang Wang
  • Robert S. Womersley

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)86-116
Journal / PublicationJournal of Approximation Theory
Volume216
Online published16 Jan 2017
Publication statusPublished - Apr 2017

Abstract

In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets—a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses for weakly isotropic random fields on Sd, d≥2. For numerical implementation, we construct a fully discrete needlet approximation of a smooth 2-weakly isotropic random field on Sd and prove that the approximation error for fully discrete needlets has the same convergence order as that for semidiscrete needlets. Numerical examples are carried out for fully discrete needlet approximations of Gaussian random fields and compared to a discrete version of the truncated Fourier expansion.

Research Area(s)

  • Gaussian, Isotropic random fields, Multiscale, Needlets, Sphere

Citation Format(s)

Needlet approximation for isotropic random fields on the sphere. / Le Gia, Quoc T.; Sloan, Ian H.; Wang, Yu Guang et al.
In: Journal of Approximation Theory, Vol. 216, 04.2017, p. 86-116.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review