On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **

Usama Elahi; Zubair Khalid; Rodney Kennedy

doi:10.1109/ICSPCS.2017.8270506

On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **

Usama Elahi, Zubair Khalid, Rodney Kennedy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we present a mathematical framework for the interpolation (approximation) of signals defined on the sphere using the notion of reproducing-kernel Hilbert spaces (RKHS) and evaluate the performance of different isotropic kernels. Using the reproducing kernel and kernel inclusion properties of RKHS, we first present the formulation for the interpolation (approximation) of a signal on the sphere from its measurements. Later, we analyse the performance of different isotropic univariate kernels: Abel Poisson kernel, Von Mises-Fisher kernel, Legendre generating function and Lebedev kernel, by evaluating the signal interpolation accuracy.

Original language	English
Title of host publication	2017, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Proceedings
Editors	Wysocki TA, Wysocki BJ
Place of Publication	Red Hook, NY
Publisher	IEEE
Pages	1-7
Edition	Peer reviewed
ISBN (Print)	9781538628874
DOIs	https://doi.org/10.1109/ICSPCS.2017.8270506
Publication status	Published - 2017
Event	11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Surfers Paradise, Australia Duration: 1 Jan 2017 → … https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8262702

Conference

Conference	11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017
Period	1/01/17 → …
Other	13 December 2017 through 15 December 2017
Internet address	https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8262702

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10.1109/ICSPCS.2017.8270506

Cite this

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title = "On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **",

abstract = "In this paper, we present a mathematical framework for the interpolation (approximation) of signals defined on the sphere using the notion of reproducing-kernel Hilbert spaces (RKHS) and evaluate the performance of different isotropic kernels. Using the reproducing kernel and kernel inclusion properties of RKHS, we first present the formulation for the interpolation (approximation) of a signal on the sphere from its measurements. Later, we analyse the performance of different isotropic univariate kernels: Abel Poisson kernel, Von Mises-Fisher kernel, Legendre generating function and Lebedev kernel, by evaluating the signal interpolation accuracy.",

author = "Usama Elahi and Zubair Khalid and Rodney Kennedy",

year = "2017",

doi = "10.1109/ICSPCS.2017.8270506",

language = "English",

isbn = "9781538628874",

pages = "1--7",

editor = "{Wysocki TA, Wysocki BJ}",

booktitle = "2017, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Proceedings",

publisher = "IEEE",

edition = "Peer reviewed",

note = "11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 ; Conference date: 01-01-2017",

url = "https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8262702",

}

Elahi, U, Khalid, Z & Kennedy, R 2017, On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **. in WTAWBJ (ed.), 2017, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Proceedings. Peer reviewed edn, IEEE, Red Hook, NY, pp. 1-7, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017, 1/01/17. https://doi.org/10.1109/ICSPCS.2017.8270506

On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **. / Elahi, Usama; Khalid, Zubair; Kennedy, Rodney.
2017, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Proceedings. ed. / Wysocki TA, Wysocki BJ. Peer reviewed. ed. Red Hook, NY: IEEE, 2017. p. 1-7.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **

AU - Elahi, Usama

AU - Khalid, Zubair

AU - Kennedy, Rodney

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N2 - In this paper, we present a mathematical framework for the interpolation (approximation) of signals defined on the sphere using the notion of reproducing-kernel Hilbert spaces (RKHS) and evaluate the performance of different isotropic kernels. Using the reproducing kernel and kernel inclusion properties of RKHS, we first present the formulation for the interpolation (approximation) of a signal on the sphere from its measurements. Later, we analyse the performance of different isotropic univariate kernels: Abel Poisson kernel, Von Mises-Fisher kernel, Legendre generating function and Lebedev kernel, by evaluating the signal interpolation accuracy.

AB - In this paper, we present a mathematical framework for the interpolation (approximation) of signals defined on the sphere using the notion of reproducing-kernel Hilbert spaces (RKHS) and evaluate the performance of different isotropic kernels. Using the reproducing kernel and kernel inclusion properties of RKHS, we first present the formulation for the interpolation (approximation) of a signal on the sphere from its measurements. Later, we analyse the performance of different isotropic univariate kernels: Abel Poisson kernel, Von Mises-Fisher kernel, Legendre generating function and Lebedev kernel, by evaluating the signal interpolation accuracy.

U2 - 10.1109/ICSPCS.2017.8270506

DO - 10.1109/ICSPCS.2017.8270506

M3 - Conference contribution

SN - 9781538628874

SP - 1

EP - 7

BT - 2017, 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017 - Proceedings

A2 - null, Wysocki TA, Wysocki BJ

PB - IEEE

CY - Red Hook, NY

T2 - 11th International Conference on Signal Processing and Communication Systems, ICSPCS 2017

Y2 - 1 January 2017

ER -

On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces **

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