Iterative method to compute the maximal concentration Slepian band-limited eigenfunction on the sphere

Zubair Khalid, Rodney Kennedy

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

    Abstract

    The Slepian concentration problem on the sphere to maximize the energy concentration of a band-limited (in spherical harmonic degree) function is formulated as an eigenvalue problem, the solution of which gives rise to a family of band-limited eigenfunctions with optimal energy concentration in the spatial region on the sphere. In the family of band-limited eigenfunctions, the most concentrated (in the spatial region) eigenfunction is used for spatial windowing and spatial smoothing. We develop an iterative method to accurately compute the most concentrated band-limited Slepian eigenfunction for a given band-limit and a spatial region of interest. Taking into account the computational issues around the proposed iterative method, we also present the procedure for the practical implementation of the proposed method. In comparison to the computation of most concentration eigenfunction by the eigenvalue decomposition which gives a family of eigenfunction, the proposed method is computationally feasible even for large band-limits. Through examples, we also show that the proposed method attains sufficient numerical accuracy.
    Original languageEnglish
    Title of host publication2014, 8th International Conference on Signal Processing and Communication Systems, ICSPCS 2014 - Proceedings
    Editorscki B.J.Wysocki T.A.
    Place of PublicationOnline
    PublisherIEEE
    Pages1-8pp
    EditionPeer Reviewed
    ISBN (Print)9781479952557
    DOIs
    Publication statusPublished - 2014
    Event8th International Conference on Signal Processing and Communication Systems, ICSPCS 2014 - Gold Coast, Australia, Australia
    Duration: 1 Jan 2014 → …

    Conference

    Conference8th International Conference on Signal Processing and Communication Systems, ICSPCS 2014
    Country/TerritoryAustralia
    Period1/01/14 → …
    OtherDecember 15-17 2014

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