Sampling great circles at their rate of innovation
In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an approp...
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Main Authors: | , |
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Other Authors: | |
Format: | Conference or Workshop Item |
Language: | English |
Published: |
2014
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Subjects: | |
Online Access: | https://hdl.handle.net/10356/100670 http://hdl.handle.net/10220/18606 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an appropriate sampling scheme. Moreover, we argue that the number of samples can be reduced to 2K(4K − 1) while maintaining accurate results. This argument is supported by our numerical results. To improve the robustness to noise of our approach, we propose a modification that uses all the available information, instead of the critical amount. The increase in accuracy is demonstrated using numerical simulations. |
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