A fast butterfly algorithm for generalized Radon transforms
Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society of Exploration Geophysicists
2013
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| Online Access: | http://hdl.handle.net/1721.1/81405 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1811085544480833536 |
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| author | Hu, Jingwei Fomel, Sergey Demanet, Laurent Ying, Lexing |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hu, Jingwei Fomel, Sergey Demanet, Laurent Ying, Lexing |
| author_sort | Hu, Jingwei |
| collection | MIT |
| description | Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N[superscript 2] log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration. |
| first_indexed | 2024-09-23T13:11:16Z |
| format | Article |
| id | mit-1721.1/81405 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:11:16Z |
| publishDate | 2013 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/814052022-09-28T12:29:33Z A fast butterfly algorithm for generalized Radon transforms Hu, Jingwei Fomel, Sergey Demanet, Laurent Ying, Lexing Massachusetts Institute of Technology. Department of Mathematics Demanet, Laurent Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N[superscript 2] log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration. Texas Consortium for Computational Seismology 2013-10-16T14:55:03Z 2013-10-16T14:55:03Z 2013-06 2012-07 Article http://purl.org/eprint/type/JournalArticle 0016-8033 1942-2156 http://hdl.handle.net/1721.1/81405 Hu, Jingwei, Sergey Fomel, Laurent Demanet, and Lexing Ying. “A fast butterfly algorithm for generalized Radon transforms.” GEOPHYSICS 78, no. 4 (June 21, 2013): U41-U51. © 2013 Society of Exploration Geophysicists https://orcid.org/0000-0001-7052-5097 en_US http://dx.doi.org/10.1190/geo2012-0240.1 Geophysics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society of Exploration Geophysicists Society of Exploration Geophysicists |
| spellingShingle | Hu, Jingwei Fomel, Sergey Demanet, Laurent Ying, Lexing A fast butterfly algorithm for generalized Radon transforms |
| title | A fast butterfly algorithm for generalized Radon transforms |
| title_full | A fast butterfly algorithm for generalized Radon transforms |
| title_fullStr | A fast butterfly algorithm for generalized Radon transforms |
| title_full_unstemmed | A fast butterfly algorithm for generalized Radon transforms |
| title_short | A fast butterfly algorithm for generalized Radon transforms |
| title_sort | fast butterfly algorithm for generalized radon transforms |
| url | http://hdl.handle.net/1721.1/81405 https://orcid.org/0000-0001-7052-5097 |
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