Inverse Multiscale Discrete Radon Transform by Filtered Backprojection
The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the fi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/1/22 |
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| author | José G. Marichal-Hernández Ricardo Oliva-García Óscar Gómez-Cárdenes Iván Rodríguez-Méndez José M. Rodríguez-Ramos |
| author_facet | José G. Marichal-Hernández Ricardo Oliva-García Óscar Gómez-Cárdenes Iván Rodríguez-Méndez José M. Rodríguez-Ramos |
| author_sort | José G. Marichal-Hernández |
| collection | DOAJ |
| description | The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods. |
| first_indexed | 2024-03-10T13:51:53Z |
| format | Article |
| id | doaj.art-f83570c1ec51422eb6b697ded7846919 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T13:51:53Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-f83570c1ec51422eb6b697ded78469192023-11-21T02:06:01ZengMDPI AGApplied Sciences2076-34172020-12-011112210.3390/app11010022Inverse Multiscale Discrete Radon Transform by Filtered BackprojectionJosé G. Marichal-Hernández0Ricardo Oliva-García1Óscar Gómez-Cárdenes2Iván Rodríguez-Méndez3José M. Rodríguez-Ramos4Industrial Engineering Department, Universidad de La Laguna, ESIT, 38200 La Laguna, SpainWooptix S.L., Avenida Trinidad, 61, 38204 La Laguna, SpainWooptix S.L., Avenida Trinidad, 61, 38204 La Laguna, SpainIndustrial Engineering Department, Universidad de La Laguna, ESIT, 38200 La Laguna, SpainIndustrial Engineering Department, Universidad de La Laguna, ESIT, 38200 La Laguna, SpainThe Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.https://www.mdpi.com/2076-3417/11/1/22inverse radon transformdiscrete radon transformfiltered backprojectionEM imaging |
| spellingShingle | José G. Marichal-Hernández Ricardo Oliva-García Óscar Gómez-Cárdenes Iván Rodríguez-Méndez José M. Rodríguez-Ramos Inverse Multiscale Discrete Radon Transform by Filtered Backprojection Applied Sciences inverse radon transform discrete radon transform filtered backprojection EM imaging |
| title | Inverse Multiscale Discrete Radon Transform by Filtered Backprojection |
| title_full | Inverse Multiscale Discrete Radon Transform by Filtered Backprojection |
| title_fullStr | Inverse Multiscale Discrete Radon Transform by Filtered Backprojection |
| title_full_unstemmed | Inverse Multiscale Discrete Radon Transform by Filtered Backprojection |
| title_short | Inverse Multiscale Discrete Radon Transform by Filtered Backprojection |
| title_sort | inverse multiscale discrete radon transform by filtered backprojection |
| topic | inverse radon transform discrete radon transform filtered backprojection EM imaging |
| url | https://www.mdpi.com/2076-3417/11/1/22 |
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