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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.


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Experimental setup and definition of variables.
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fig1: Experimental setup and definition of variables.

Mentions: Consider a 2D object in which a nonuniform radioactivity source distribution exists and is represented by a nonnegative integrable function f(x, y) with bounded support. Figure 1 shows how a collimated linear detector is set parallel to the plane of the object and how it collects only outgoing radiation from the object which is parallel to the direction of the collimator holes.


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

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

Experimental setup and definition of variables.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Experimental setup and definition of variables.
Mentions: Consider a 2D object in which a nonuniform radioactivity source distribution exists and is represented by a nonnegative integrable function f(x, y) with bounded support. Figure 1 shows how a collimated linear detector is set parallel to the plane of the object and how it collects only outgoing radiation from the object which is parallel to the direction of the collimator holes.

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