The Mathematical Foundations of 3D Compton Scatter Emission Imaging

Truong, T.T.; Nguyen, Maï K.; Zaidi, Habib

doi:10.1155/2007/92780

Cited by 43 publications

(48 citation statements)

References 35 publications

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“…The measured photon flux density at the detector site is a sum of conical projections (Fig. 3) and is called compounded conical projections [22], [23]. It should be noted that data acquisition no longer requires to rotate the detector in space (as it is done in a conventional emission imaging).…”

Section: How Are Scattered Photons Used?mentioning

confidence: 99%

“…The mathematical expression of one arbitrary conical projection is quite involved and given in [23]. The summation over all such objects can be still expressed as a linear integral transform of the activity density (5) Unfortunately, the explicit form of is too complicated to yield a simple interpretation, and will not be addressed here.…”

Section: How To Increase Sensitivity?mentioning

confidence: 99%

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On a Novel Approach to Compton Scattered Emission Imaging

Nguyen¹,

Truong²,

Driol³

et al. 2009

IEEE Trans. Nucl. Sci.

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Abstract-Imaging processes built on the Compton scattering effect are currently under intense investigation. However, despite many innovative contributions, this topic still pose a formidable mathematical and technical challenge. In this work, we argue that, in the framework of single-photon emission imaging, collecting Compton scattered radiation from an emitting object, allows to image the radiotracer distribution in vivo. Data is acquired by a stationary collimated gamma camera under the form of compounded conical projections of the activity density function. Mathematically, the image formation process is described by the so-called Compounded Conical Radon Transform (CCRT) and three-dimensional object reconstruction is based on an inversion formula of the CCRT. We perform numerical simulations to show the feasibility of this new imaging modality, which offers the remarkable advantage of operating in stationary mode without the need of bulky and cumbersome spatial rotational mechanism of conventional gamma cameras. This is highly attractive for applications in medical imaging, industrial non-destructive evaluation, nuclear waste storage surveillance and homeland security monitoring. Finally, to improve drastically the sensitivity, we introduce a new feature allowing to acquire data without mechanical collimation and support the findings with some preliminary simulation results.

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Section: How Are Scattered Photons Used?mentioning

confidence: 99%

Section: How To Increase Sensitivity?mentioning

confidence: 99%

On a Novel Approach to Compton Scattered Emission Imaging

Nguyen¹,

Truong²,

Driol³

et al. 2009

IEEE Trans. Nucl. Sci.

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“…Several inversion formulas for various types of cone transforms were derived in [2,5,6,11,12,13,16,19,21,24,25,28,31,34]. The cone transform with planar vertex positions and a fixed central axis was studied in [5,6,16,21,24,25,34].…”

Section: Introductionmentioning

confidence: 99%

“…The cone transform with planar vertex positions and a fixed central axis was studied in [5,6,16,21,24,25,34]. Haltme ier derived an exact backprojection-type inversion formula for the n-dimensional cone transform which integrates a given n-dimensional function over all conical surfaces having vertices on a hyperplane and a central axis orthogonal to this hyperplane in [13].…”

Section: Introductionmentioning

confidence: 99%

Exact Inversion of the Cone Transform Arising in an Application of a Compton Camera Consisting of Line Detectors

Jung¹,

Moon²

2016

SIAM J. Imaging Sci.

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Abstract.A Compton camera has been suggested for use in single photon emission computed tomography because a conventional gamma camera has low efficiency. Here we consider a cone transform brought about by a Compton camera with line detectors. A cone transform takes a given function on the 3-dimensional space and assigns to it the surface integral of the function over cones determined by the 1-dimensional vertex space, the 1-dimensional central axis, and the 1-dimensional opening angle. We generalize this cone transform to n-dimensional space and provide an inversion formula. Also, numerical simulations are presented to demonstrate our suggested algorithm in three dimensions.Key words. Compton camera, SPECT, tomography, cone transform, inversion, gamma camera AMS subject classifications. 44A12, 65R10, 92C55DOI. 10.1137/15M10336171. Introduction. A Radon-type transform that assigns to a given function its surface integral over various sets of cones has been studied, since it is known that this kind of a transform relates to a Compton camera. A Compton camera, also called an electronically collimated γ-camera, was introduced for use in single photon emission computed tomography (SPECT) because of the low efficiency of a conventional γ-camera [26,32]. A Compton camera has very high sensitivity and flexibility of geometrical design, so it has attracted a lot of interest and applications in many areas including monitoring nuclear power plants and astronomy [1,3].A standard Compton camera consists of two planar detectors: a scatter detector and an absorption detector, positioned one behind the other. A photon emitted from a radioactive source toward the camera undergoes Compton scattering in the scatter detector, and is absorbed in the absorption detector positioned behind (see Figure 1). In each detector, the position of the hit and the energy of the photon are measured. The scattering angle or the

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“…However this Basko transform is in fact a V-line Radon transform with swinging axis around a detection site whereas the one considered here has a fixed axis direction [4]. The Vline Radon transform is also considered as a two-dimensional version of the Conical Radon Transform (CRT ) which have been introduced some years ago ( [5], [10], [11], [12], [13]). These generalized Radon transforms (T V and CRT ) have numerous applications in imaging science, in particular in new Compton scattering emission imaging ( [4], [5], [6], [7], [8], [10], [11], [12], [13]).…”

Section: Introductionmentioning

confidence: 99%

A novel coupled transmission-reflection tomography and the V-line Radon transform

Régnier¹,

Nguyen-Verger²

2011

2011 18th IEEE International Conference on Image Processing

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The Radon transform (RT ) on straight lines deals as mathematical foundation for conventional tomographic imaging (e.g. X-ray scanner, Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET)) which use only one physical phenomenon, i.e. either transmission or emission of radiation. An imaging concept exploiting jointly two phenomena leads to a Radon transform defined on a geometrical support different from straight lines. In this paper, we propose a new two-dimensional X-ray imaging based on the coupling between transmission and reflection. Its modeling leads to a Radon transform defined on a pair of half-lines forming a vertical letter V, called V-line RT (V -RT ). Moreover we establish the analytic inverse formula of this new transform, which forms the mathematical basis for image reconstruction. Through simulations, image formation and reconstruction results show the feasibility of this new imaging. The main advantage is the use of an one-dimensional detector which does not rotate for two-dimensional image reconstruction.

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The Mathematical Foundations of 3D Compton Scatter Emission Imaging

Cited by 43 publications

References 35 publications

On a Novel Approach to Compton Scattered Emission Imaging

On a Novel Approach to Compton Scattered Emission Imaging

Exact Inversion of the Cone Transform Arising in an Application of a Compton Camera Consisting of Line Detectors

A novel coupled transmission-reflection tomography and the V-line Radon transform

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