TY - GEN

T1 - Accurate Reconstruction of Finite Rate of Innovation Signals on the Sphere

AU - Sattar, Yahya

AU - Khalid, Zubair

AU - Kennedy, Rodney A.

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - Unit sphere

KW - finite rate of innovation

KW - sampling

KW - signal reconstruction

KW - spherical harmonic transform

UR - http://www.scopus.com/inward/record.url?scp=85068974263&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2019.8682607

DO - 10.1109/ICASSP.2019.8682607

M3 - Conference contribution

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 1727

EP - 1731

BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019

Y2 - 12 May 2019 through 17 May 2019

ER -