Combined Modalities of Compton Scattering Tomography

Rigaud, Gaël; Régnier, Rémi; Nguyen, Maï K.; Zaidi, Habib

doi:10.1109/tns.2013.2252022

Cited by 9 publications

(5 citation statements)

References 18 publications

(24 reference statements)

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“…Although such an assumption is reasonable for high energies and soft materials, the photoelectric absorption is not negligible for low energies (for instance in the case E 0 = 140 keV in our simulations above). However, one can proceed as in [46], i.e. use clustering techniques (such as K-means) to segment the electron density in terms of materials at each iteration.…”

Section: Discussionmentioning

confidence: 99%

Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Rigaud

Hahn

2020

Inverse Problems in Science and Engineering

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Compton scattering describes the scattering of a photon after its collision with an electron. The recent developments of spectral cameras, able to collect photons in terms of energy, open the way to a new imaging concept: 3D Compton scattering imaging (CSI), which seeks to exploit the scattered radiation as a vector of information while a specimen of interest is illuminated by a monochromatic ionizing source. Focusing on modelling the first-order scattering, image reconstruction from CSI data remains a difficult challenge. In particular, physical constraints (detector and architecture of the scanner) lead to various incompleteness scenario within the data and thus streak artifacts when using filtered backprojection type formulas. This paper addresses the problem of recovering an object under study using CSI data subject to incompleteness and assuming only first-order scattering. The proposed method consists of suitably tuning the multiplicative Kaczmarz algorithm and is implemented and tested for two architectures of the scanner. Furthermore, the modality on CSI considered here presents the advantage of not requiring any rotation of the source or object.

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Section: Discussionmentioning

confidence: 99%

Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Rigaud

Hahn

2020

Inverse Problems in Science and Engineering

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“…The second CST modality, proposed by Nguyen and Truong [7,14,13], is composed of a pair source -detector diametrically opposed on a circle. This system has lead to a CART based on circular arcs having a chord of fixed length.…”

Section: Basics Of Compton Scattering Tomography (Cst)mentioning

confidence: 99%

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography

Tarpau¹,

Cebeiro²,

Nguyen³

et al. 2019

Preprint

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In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST) which is made of a single detector rotating around a fixed source. Unlike some previous CST no collimator is used at the detector, such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inverse formula is established for this new Radon transform. This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency condition in Cormacks sense. Moreover, a fast and efficient numerical implementation via an alternative formulation based on Hilbert transform is carried out. Simulation results illustrate the theoretical feasibility of the new system. From a practical point of view, a collimator-free system considerably increases the amount of data, which is particularly significant in a scatter imaging system.

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“…In the examples we present below, we do not take into account the attenuation factor. However, interested readers could look at some iterative correction algorithm (for example [17]) to perform image reconstruction in attenuated cases.…”

Section: Analytical Modeling and Realistic Expressionmentioning

confidence: 99%

On the inversion of the Radon transform on a generalized Cormack-type class of curves

Rigaud¹

2013

Inverse Problems

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In 1981 Cormack studied the Radon transform defined on a family of curves and showed their inversion through their circular harmonic expansions. In this paper we propose to extend this property to a more general family of curves which are defined by a nonlinear-first-order differential equation. In particular we focus on a subclass of this family for which the singular value decomposition shown by Cormack in 1964 can be generalized. Applications based on this subclass clearly appear since the Radon transform defined on three kinds of its curves may serve to model three different Compton scattering tomography modalities. Simulation results using analytical inversions and Chebyshev/Zernike expansions for these three Radon transform show the strength and the validation of proposed inversion methods.

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Combined Modalities of Compton Scattering Tomography

Cited by 9 publications

References 18 publications

Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography

On the inversion of the Radon transform on a generalized Cormack-type class of curves

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