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.

Date Published: 26 September 2013
PDF: 10 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88580V (26 September 2013); doi: 10.1117/12.2023863

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)