Spherical harmonics and Earth-rotation synthesis in radio astronomy

MacPhie, R.H.; Okongwu, E.

doi:10.1109/tap.1975.1141085

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…Using the definition of associated Legendre polynomials in (5), we rewrite the spherical harmonics (3) as…”

Section: B the Data Matrixmentioning

confidence: 99%

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Sampling Sparse Signals on the Sphere: Algorithms and Applications

Lu¹

2016

IEEE Trans. Signal Process.

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We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool widely used in array signal processing and finite-rate-of-innovation (FRI) sampling. The proposed algorithm can reconstruct $K$ spikes from $(K+\sqrt{K})^2$ spatial samples. This sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four for large $K$. We showcase the versatility of the proposed algorithm by applying it to three different problems: 1) sampling diffusion processes induced by localized sources on the sphere, 2) shot noise removal, and 3) sound source localization (SSL) by a spherical microphone array. In particular, we show how SSL can be reformulated as a spherical sparse sampling problem.Comment: 14 pages, 8 figures, submitted to IEEE Transactions on Signal Processin

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“…Using the definition of associated Legendre polynomials in (5), we rewrite the spherical harmonics (3) as…”

Section: B the Data Matrixmentioning

confidence: 99%

“…Take, for example, any signal defined on Earth's surface [1]- [3]. Signals from space measured on Earth [4], [5] also have a spherical domain. In acoustics, spherical microphone arrays output a time-varying signal supported on a sphere [6], [7], while in diffusion weighted magnetic resonance imaging fiber orientations live on a sphere [8].…”

Section: Introductionmentioning

confidence: 99%

Sampling Sparse Signals on the Sphere: Algorithms and Applications

Lu¹

2016

IEEE Trans. Signal Process.

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“…Examples are signals defined on Earth's surface [1][2][3], signals from space measured on Earth [4,5], or spherical microphone arrays that output a time-varying signal supported on a sphere [6,7].…”

Section: Introductionmentioning

confidence: 99%

Sampling spherical finite rate of innovation signals

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpassfiltered observations. The proposed algorithm can reconstruct K spikes from (K + √ K) 2 spatial samples, thus improving over previously known FRI sampling schemes on the sphere by a factor of up to four. Further, we show how multiple sound source localization (SSL) by a spherical microphone array can be transformed into a spherical FRI sampling problem. We certify the effectiveness of the proposed algorithm by using it to solve the SSL problem.

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