Accurate Reconstruction of Finite Rate of Innovation Signals on the Sphere

Yahya Sattar, Zubair Khalid, Rodney A. Kennedy

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

    1 Citation (Scopus)

    Abstract

    We propose a method for the accurate and robust reconstruction of the non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based method for the accurate recovery of parameters of the Dirac functions using a finite number of observations of the bandlimited signal. In comparison to existing techniques, the proposed method enables more accurate reconstruction primarily due to the better conditioning of systems involved in the recovery of parameters. In order to reconstruct K Diracs on the sphere, the proposed method requires samples of the signal bandlimited in the spherical harmonic ({\text{SH}}) domain at SH degree equal or greater than K + \sqrt {K + \frac{1}{4}} - \frac{1}{2}. In comparison to the existing state-of-the-art technique, the required bandlimit, and consequently the number of samples, of the proposed method is (approximately) the same. We also conduct numerical experiments to demonstrate that the proposed technique is more accurate than the existing methods by a factor of {10^7} or more for 2 \leq K \leq 20.

    Original languageEnglish
    Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1727-1731
    Number of pages5
    ISBN (Electronic)9781479981311
    DOIs
    Publication statusPublished - May 2019
    Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
    Duration: 12 May 201917 May 2019

    Publication series

    NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
    Volume2019-May
    ISSN (Print)1520-6149

    Conference

    Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
    Country/TerritoryUnited Kingdom
    CityBrighton
    Period12/05/1917/05/19

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