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...
| 主要な著者: | , |
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| その他の著者: | |
| フォーマット: | Conference Paper |
| 言語: | English |
| 出版事項: |
2014
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| 主題: | |
| オンライン･アクセス: | https://hdl.handle.net/10356/100670 http://hdl.handle.net/10220/18606 |
| _version_ | 1826127437958742016 |
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| author | Deslauriers-Gauthier, Samuel Marziliano, Pina |
| author2 | Van De Ville, Dimitri |
| author_facet | Van De Ville, Dimitri Deslauriers-Gauthier, Samuel Marziliano, Pina |
| author_sort | Deslauriers-Gauthier, Samuel |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:08:33Z |
| format | Conference Paper |
| id | ntu-10356/100670 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:08:33Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1006702020-03-07T13:24:50Z Sampling great circles at their rate of innovation Deslauriers-Gauthier, Samuel Marziliano, Pina Van De Ville, Dimitri Papadakis, Manos Goyal, Vivek K. School of Electrical and Electronic Engineering Wavelets and Sparsity (15th : 2013 : San Diego, USA) DRNTU::Engineering::Electrical and electronic engineering::Antennas, wave guides, microwaves, radar, radio 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. Published version 2014-01-16T06:47:05Z 2019-12-06T20:26:17Z 2014-01-16T06:47:05Z 2019-12-06T20:26:17Z 2013 2013 Conference Paper Deslauriers-Gauthier, S., & Marziliano, P. (2013). Sampling great circles at their rate of innovation. Wavelets and Sparsity XV, 8858. https://hdl.handle.net/10356/100670 http://hdl.handle.net/10220/18606 10.1117/12.2023863 en © 2013 SPIE. This paper was published in Wavelets and Sparsity XV and is made available as an electronic reprint (preprint) with permission of SPIE. The paper can be found at the following official DOI: [http://dx.doi.org/10.1117/12.2023863]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering::Antennas, wave guides, microwaves, radar, radio Deslauriers-Gauthier, Samuel Marziliano, Pina Sampling great circles at their rate of innovation |
| title | Sampling great circles at their rate of innovation |
| title_full | Sampling great circles at their rate of innovation |
| title_fullStr | Sampling great circles at their rate of innovation |
| title_full_unstemmed | Sampling great circles at their rate of innovation |
| title_short | Sampling great circles at their rate of innovation |
| title_sort | sampling great circles at their rate of innovation |
| topic | DRNTU::Engineering::Electrical and electronic engineering::Antennas, wave guides, microwaves, radar, radio |
| url | https://hdl.handle.net/10356/100670 http://hdl.handle.net/10220/18606 |
| work_keys_str_mv | AT deslauriersgauthiersamuel samplinggreatcirclesattheirrateofinnovation AT marzilianopina samplinggreatcirclesattheirrateofinnovation |