Computed Tomography Reconstruction Using Only One Projection Angle
Let <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> represent a digitized version of an image <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula>. Assume that...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10026319/ |
| _version_ | 1797804870790545408 |
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| author | Fawaz Hjouj Mohamed Soufiane Jouini |
| author_facet | Fawaz Hjouj Mohamed Soufiane Jouini |
| author_sort | Fawaz Hjouj |
| collection | DOAJ |
| description | Let <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> represent a digitized version of an image <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula>. Assume that the image fits inside a rectangular region and this region is subdivided into <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> squares. We call these squares the shifted box functions. Thus <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula> is approximated by <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> matrix <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula>. This paper proofs that <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> can be recovered exactly and uniquely from the Radon transform of <inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> using only one selected view angle with a well selected family of <inline-formula> <tex-math notation="LaTeX">$MN$ </tex-math></inline-formula> lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography. |
| first_indexed | 2024-03-13T05:43:33Z |
| format | Article |
| id | doaj.art-39b0aed609b44fada4293336e6edaee7 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T05:43:33Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-39b0aed609b44fada4293336e6edaee72023-06-13T20:32:29ZengIEEEIEEE Access2169-35362023-01-01119672967910.1109/ACCESS.2023.323995610026319Computed Tomography Reconstruction Using Only One Projection AngleFawaz Hjouj0https://orcid.org/0000-0001-8859-3784Mohamed Soufiane Jouini1https://orcid.org/0000-0001-9741-0636Department of Mathematics, Khalifa University, Abu Dhabi, United Arab EmiratesDepartment of Mathematics, Khalifa University, Abu Dhabi, United Arab EmiratesLet <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> represent a digitized version of an image <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula>. Assume that the image fits inside a rectangular region and this region is subdivided into <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> squares. We call these squares the shifted box functions. Thus <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula> is approximated by <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> matrix <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula>. This paper proofs that <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> can be recovered exactly and uniquely from the Radon transform of <inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> using only one selected view angle with a well selected family of <inline-formula> <tex-math notation="LaTeX">$MN$ </tex-math></inline-formula> lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography.https://ieeexplore.ieee.org/document/10026319/Algebraic reconstructionradon transformtomographylimited data tomography |
| spellingShingle | Fawaz Hjouj Mohamed Soufiane Jouini Computed Tomography Reconstruction Using Only One Projection Angle IEEE Access Algebraic reconstruction radon transform tomography limited data tomography |
| title | Computed Tomography Reconstruction Using Only One Projection Angle |
| title_full | Computed Tomography Reconstruction Using Only One Projection Angle |
| title_fullStr | Computed Tomography Reconstruction Using Only One Projection Angle |
| title_full_unstemmed | Computed Tomography Reconstruction Using Only One Projection Angle |
| title_short | Computed Tomography Reconstruction Using Only One Projection Angle |
| title_sort | computed tomography reconstruction using only one projection angle |
| topic | Algebraic reconstruction radon transform tomography limited data tomography |
| url | https://ieeexplore.ieee.org/document/10026319/ |
| work_keys_str_mv | AT fawazhjouj computedtomographyreconstructionusingonlyoneprojectionangle AT mohamedsoufianejouini computedtomographyreconstructionusingonlyoneprojectionangle |