Limits...
On the v-line radon transform and its imaging applications.

Morvidone M, Nguyen MK, Truong TT, Zaidi H - Int J Biomed Imaging (2010)

Bottom Line: 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.We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure.We illustrate the working principles of this imaging modality by presenting numerical simulation results.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, France.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus

FBP-IM reconstruction of the thyroid phantom with dω = 0.005 rad.
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fig4: FBP-IM reconstruction of the thyroid phantom with dω = 0.005 rad.

Mentions: We present now the results of numerical simulations. The original image (Figure 2) of size 512 × 512 of length units is a thyroid phantom presenting with small nodules. Figure 3 shows the T𝕍 transform of a thyroid phantom with angular sampling rate dω = 0.005 rad and 314 projections (π/2/0.005 = 314) which are the images of Compton scattered radiation on the camera in terms of the distance ξ and the scattering angle ω. The reconstruction using FBP is given in Figure 4. The artifacts are due to the limited number of projections. Moreover, backprojection on V-lines generates more artifacts than backprojection on straight lines, because of more spurious line intersections. As our numerical results are based on the discretization of the inverse formula (22), a choice of a smaller discretization step dω would improve image quality. This is indeed a well-established fact and in agreement with the improved sampling resulting from the increase of data collected at more values of the scattering angle ω. Despite these limitations, the small structures in the object are clearly reconstructed. This result illustrates undoubtedly the feasibility of the new imaging modality, for which the main advantage resides in the use of a one-dimensional nonmoving Compton camera for two-dimensional image processing.


On the v-line radon transform and its imaging applications.

Morvidone M, Nguyen MK, Truong TT, Zaidi H - Int J Biomed Imaging (2010)

FBP-IM reconstruction of the thyroid phantom with dω = 0.005 rad.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2913536&req=5

fig4: FBP-IM reconstruction of the thyroid phantom with dω = 0.005 rad.
Mentions: We present now the results of numerical simulations. The original image (Figure 2) of size 512 × 512 of length units is a thyroid phantom presenting with small nodules. Figure 3 shows the T𝕍 transform of a thyroid phantom with angular sampling rate dω = 0.005 rad and 314 projections (π/2/0.005 = 314) which are the images of Compton scattered radiation on the camera in terms of the distance ξ and the scattering angle ω. The reconstruction using FBP is given in Figure 4. The artifacts are due to the limited number of projections. Moreover, backprojection on V-lines generates more artifacts than backprojection on straight lines, because of more spurious line intersections. As our numerical results are based on the discretization of the inverse formula (22), a choice of a smaller discretization step dω would improve image quality. This is indeed a well-established fact and in agreement with the improved sampling resulting from the increase of data collected at more values of the scattering angle ω. Despite these limitations, the small structures in the object are clearly reconstructed. This result illustrates undoubtedly the feasibility of the new imaging modality, for which the main advantage resides in the use of a one-dimensional nonmoving Compton camera for two-dimensional image processing.

Bottom Line: 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.We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure.We illustrate the working principles of this imaging modality by presenting numerical simulation results.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, France.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus