On the V-Line Radon Transform and Its Imaging Applications
Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/2010/208179 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849412540112568320 |
|---|---|
| author | M. Morvidone M. K. Nguyen T. T. Truong H. Zaidi |
| author_facet | M. Morvidone M. K. Nguyen T. T. Truong H. Zaidi |
| author_sort | M. Morvidone |
| collection | DOAJ |
| description | Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results. |
| format | Article |
| id | doaj-art-63f8283bf2ee41b99f4f9f1b44c24577 |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-63f8283bf2ee41b99f4f9f1b44c245772025-08-20T03:34:25ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962010-01-01201010.1155/2010/208179208179On the V-Line Radon Transform and Its Imaging ApplicationsM. Morvidone0M. K. Nguyen1T. T. Truong2H. Zaidi3Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, FranceLaboratoire Equipes de Traitement des Images et du Signal, CNRS UMR 8051/ENSEA, Université de Cergy-Pontoise, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, FranceLaboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, FranceDivision of Nuclear Medicine, Geneva University Hospital, 1211 Geneva 4, SwitzerlandRadon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.http://dx.doi.org/10.1155/2010/208179 |
| spellingShingle | M. Morvidone M. K. Nguyen T. T. Truong H. Zaidi On the V-Line Radon Transform and Its Imaging Applications International Journal of Biomedical Imaging |
| title | On the V-Line Radon Transform and Its Imaging Applications |
| title_full | On the V-Line Radon Transform and Its Imaging Applications |
| title_fullStr | On the V-Line Radon Transform and Its Imaging Applications |
| title_full_unstemmed | On the V-Line Radon Transform and Its Imaging Applications |
| title_short | On the V-Line Radon Transform and Its Imaging Applications |
| title_sort | on the v line radon transform and its imaging applications |
| url | http://dx.doi.org/10.1155/2010/208179 |
| work_keys_str_mv | AT mmorvidone onthevlineradontransformanditsimagingapplications AT mknguyen onthevlineradontransformanditsimagingapplications AT tttruong onthevlineradontransformanditsimagingapplications AT hzaidi onthevlineradontransformanditsimagingapplications |