Optimal-dimensionality sampling on the sphere: Improvements and variations

Date

2017

Authors

Nafees, Wajeeha
Khalid, Zubair
Kennedy, Rodney
McEwen, Jason

Journal Title

Journal ISSN

Volume Title

Publisher

IEEE

Abstract

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of freedom of the signal in the spectral (harmonic) domain. The computation of the spherical harmonic transform (SHT) associated with the optimal-dimensionality sampling requires the inversion of a series of linear systems in an iterative manner. The stability of the inversion depends on the placement of iso-latitude rings of samples along co-latitude. In this work, we have developed a method to place these iso-latitude rings of samples with the objective of improving the well-conditioning of the linear systems involved in the computation of the SHT. We also propose a multi-pass SHT algorithm to iteratively improve the accuracy of the SHT of band-limited signals. Furthermore, we review the changes in the computational complexity and improvement in accuracy of the SHT with the embedding of the proposed methods. Through numerical experiments, we illustrate that the proposed variations and improvements in the SHT algorithm corresponding to the optimal-dimensionality sampling scheme significantly enhance the accuracy of the SHT.

Description

Keywords

unit sphere, sampling, spherical harmonic transform, optimal-dimensionality, condition number minimization, harmonic analysis

Citation

Source

2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Type

Conference paper

Book Title

Entity type

Access Statement

License Rights

DOI

10.1109/SAMPTA.2017.8024464

Restricted until

2099-12-31