Abstract:In an effort to promote Compton scatter tomography (CST) as an adequate modality for imaging the inner parts of large objects limited in a half-space of R 3
AQ1, we show that the standard CST can be 'improved' in some particular sense by 'doubling' the scanning mechanism. To this end, one needs to record for each position of a detector the scattered flux densities at two energies of scattered radiation, instead of one. Curiously, thanks to geometric inversion, this 'double' scanning may be converted into a tra… Show more
“…Thus, first order Compton scattering is the only source of attenuation for radiation and data acquisition is performed with a pair source detector, assumed to be point-like. These conditions are common in the literature[18,35,36,3,31,29,27] and have been already discussed in[19,33,35,27].…”
<p style='text-indent:20px;'>In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.</p>
“…Thus, first order Compton scattering is the only source of attenuation for radiation and data acquisition is performed with a pair source detector, assumed to be point-like. These conditions are common in the literature[18,35,36,3,31,29,27] and have been already discussed in[19,33,35,27].…”
<p style='text-indent:20px;'>In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.</p>
“…Thus, first order Compton scattering is the only source of attenuation for radiation and data acquisition is performed with a pair source detector, assumed to be point-like. These conditions are common in the literature[16,26,29,30,31,20,24] and have been already discussed in[15,19,26,24].…”
In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.
“…Transmission Compton scatter tomography consists in illuminating the object under study with a source of radiation and registering the scattered photons in the neighborhood of the object. The interest in this technique is supported by its numerous potential applications namely non-destructive testing, homeland security and the study of composite materials used in aircraft industry [2,3]. Recent works in medical imaging suggest possible advantages in diagnosis since images exhibit better contrast in certain scenarios such as lung tumors [4,5].…”
Section: Introductionmentioning
confidence: 99%
“…Depending on the setup, forward models are based on integral transforms on different manifolds. When collimated detectors are used, manifolds are circular arcs [1,9,10,11,12,13] or pairs of circular arcs [2]. When collimator is removed from detectors, manifolds are toric sections [3,14].…”
Compton scattering tomography is an emerging scanning technique with attractive applications in several fields such as non-destructive testing and medical imaging. In this paper, we study a modality in three dimensions that employs a fixed source and a single detector moving on a spherical surface. We also study the Radon transform modeling the data that consists of integrals on toric surfaces. Using spherical harmonics we arrive to a generalized Abel’s type equation connecting the coefficients of the expansion of the data with those of the function. We show the uniqueness of its solution and so the invertibility of the toric Radon transform. We illustrate this through numerical reconstructions in three dimensions using a regularized approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.