Optimal-dimensionality sampling on the sphere: Improvements and variations

Wajeeha Nafees, Zubair Khalid, Rodney A. Kennedy, Jason D. McEwen

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Citation (Scopus)

    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.

    Original languageEnglish
    Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
    EditorsGholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages87-91
    Number of pages5
    ISBN (Electronic)9781538615652
    DOIs
    Publication statusPublished - 1 Sept 2017
    Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
    Duration: 3 Jul 20177 Jul 2017

    Publication series

    Name2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

    Conference

    Conference12th International Conference on Sampling Theory and Applications, SampTA 2017
    Country/TerritoryEstonia
    CityTallinn
    Period3/07/177/07/17

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