Quantum 3D FFT in Tomography
The Radon transform constitutes the conventional tool for tomosynthesis, i.e., the composition of cross-sections of an object from its projections. It is actually a version of the Fourier Transform, which is accompanied by the appropriate digital high pass filters for correct distribution of energy...
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| Format: | Article |
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MDPI AG
2023-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/6/4009 |
| _version_ | 1797613586938331136 |
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| author | Georgia Koukiou Vassilis Anastassopoulos |
| author_facet | Georgia Koukiou Vassilis Anastassopoulos |
| author_sort | Georgia Koukiou |
| collection | DOAJ |
| description | The Radon transform constitutes the conventional tool for tomosynthesis, i.e., the composition of cross-sections of an object from its projections. It is actually a version of the Fourier Transform, which is accompanied by the appropriate digital high pass filters for correct distribution of energy among the reconstructed frequency components. The Radon transform and its inverse are employed in their 2D and 3D versions, respectively, and the whole procedure is verified by the a priori known cross-sections to be reconstructed (known fandom). Usually, 3D medical image cubes, which are to be reconstructed, require powerful computational tools since the 2D projections are of high-resolution containing millions of pixels. Although the 3D FFT is very fast, the large number of projections will result in a 3D spectrum of very large dimensions. Inverting this spectrum with the inverse 3D FFT is extremely time consuming. In this work, the implementation of the 2D Radon transform using the 2D Quantum Fourier Transform is analytically presented. Simultaneously, its inverse version is realized by means of the Quantum inverse 3D FFT. For this purpose, a review of the necessary quantum computational units is presented for the implementation of the quantum 3D FFT and simultaneously simple examples of tomosynthesis are given by means of the quantum version of the 2D Radon transform and its inverse 3D counterpart. The whole procedure of the quantum tomosynthesis is analytically described. |
| first_indexed | 2024-03-11T06:58:01Z |
| format | Article |
| id | doaj.art-dc7a171a82624f75ac5a6b5d8d03d980 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T06:58:01Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-dc7a171a82624f75ac5a6b5d8d03d9802023-11-17T09:30:10ZengMDPI AGApplied Sciences2076-34172023-03-01136400910.3390/app13064009Quantum 3D FFT in TomographyGeorgia Koukiou0Vassilis Anastassopoulos1Electronics Laboratory, Physics Department, University of Patras, 26504 Patras, GreeceElectronics Laboratory, Physics Department, University of Patras, 26504 Patras, GreeceThe Radon transform constitutes the conventional tool for tomosynthesis, i.e., the composition of cross-sections of an object from its projections. It is actually a version of the Fourier Transform, which is accompanied by the appropriate digital high pass filters for correct distribution of energy among the reconstructed frequency components. The Radon transform and its inverse are employed in their 2D and 3D versions, respectively, and the whole procedure is verified by the a priori known cross-sections to be reconstructed (known fandom). Usually, 3D medical image cubes, which are to be reconstructed, require powerful computational tools since the 2D projections are of high-resolution containing millions of pixels. Although the 3D FFT is very fast, the large number of projections will result in a 3D spectrum of very large dimensions. Inverting this spectrum with the inverse 3D FFT is extremely time consuming. In this work, the implementation of the 2D Radon transform using the 2D Quantum Fourier Transform is analytically presented. Simultaneously, its inverse version is realized by means of the Quantum inverse 3D FFT. For this purpose, a review of the necessary quantum computational units is presented for the implementation of the quantum 3D FFT and simultaneously simple examples of tomosynthesis are given by means of the quantum version of the 2D Radon transform and its inverse 3D counterpart. The whole procedure of the quantum tomosynthesis is analytically described.https://www.mdpi.com/2076-3417/13/6/4009Quantum Fourier Transformquantum circuitstomographyradon transformquantum 3D back projection |
| spellingShingle | Georgia Koukiou Vassilis Anastassopoulos Quantum 3D FFT in Tomography Applied Sciences Quantum Fourier Transform quantum circuits tomography radon transform quantum 3D back projection |
| title | Quantum 3D FFT in Tomography |
| title_full | Quantum 3D FFT in Tomography |
| title_fullStr | Quantum 3D FFT in Tomography |
| title_full_unstemmed | Quantum 3D FFT in Tomography |
| title_short | Quantum 3D FFT in Tomography |
| title_sort | quantum 3d fft in tomography |
| topic | Quantum Fourier Transform quantum circuits tomography radon transform quantum 3D back projection |
| url | https://www.mdpi.com/2076-3417/13/6/4009 |
| work_keys_str_mv | AT georgiakoukiou quantum3dfftintomography AT vassilisanastassopoulos quantum3dfftintomography |