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

In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system 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 associated Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inversion 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 conditions in Cormack's 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, an uncollimated detector system considerably increases the amount of collected data, which is particularly significant in a scatter imaging system.Comment: 14 pages, 5 figure

A new bi-imaging NDT system for simultaneous recovery of attenuation and electronic density maps

Computed Tomography is a widely used imaging technique for non-destructive testing and evaluation in industry. Tomographic modalities exploit only primary radiation, which is non-deviated but attenuated radiation going through matter. However, in the energy range of X and gamma rays used in non destructive testing, Compton effect is an important physical phenomenon which should be taken into account. Compton Scattering Tomography is precisely theimaging technique, which not only accounts for the Compton effect but also uses it to image material electronic density. This paper proposes the concept of a Compton scanner,which is formed by a source and several detectors placed on a circular ring. When the detectors are set to register the energy of primary photons, the system works as Fan-Beam computed tomography scanner. But if the detectors are set to register the energy of scattered photons, the system operates as Compton scattering tomography scanner. Such a device, that we called a bi-imaging system provides both the attenuation map and the electronic density of the scanned object. Both information from primary and scattered rays is then wisely exploited. The mathematical modelling of this system makes use of a Radon transform on circular arcs. Numerical simulations are carried out in order to illustrate the theoretical feasibility of the proposed system.Fil: Tarpau, Cecilia. Cergy-paris Universite (cergy-paris Universite); Francia. Université de Versailles Saint-quentin-en-yvelines.; FranciaFil: Cebeiro, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnología. Centro de Matemática Aplicada; ArgentinaFil: Nguyen, Mai K.. Cergy-paris Universite (cergy-paris Universite); Francia11th International Symposium on Non-Destructive Testing and Evaluation in AerospaceParisFranciaConfédération Française pour les Essais Non Destructif

A new Compton scattering tomography and its applications in medical imaging

International audienceCompton Scatter Imaging stands out among the novel approaches for exploring the inner parts of bodies because it takes advantage of scattered radiation. Instead of being rejected, as it is in current systems, scattered radiation is used as an imaging agent improving sensitivity and potentially reducing the amount of radiation required. Compton Scatter modalities have complex theoretical foundations involving Radon transforms in different manifolds. Several Compton based systems have been proposed and continue being studied including transmission and emission techniques and combinations of them like the new bimodal emission/transmission systems. Recently, a numerical study of a new modality of Compton tomography has been performed revealing attractive features in the field of non destructive testing of large objects like reinforced concrete or metal rafters. In this text, we complete this analysis studying its application in biomedical imaging. We analyse quality, with testing images intended for biomedical imaging, aswell as applications. Our results may help to develop new reconstruction techniques for bimodal images

Radon transforms on circular arcs and their associated modalities of Compton Scattering Tomography

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A new bi-imaging NDT system for simultaneous recovery of attenuation and electronic density maps

International audienc

The Radon transform on V-lines: artifact analysis and image enhancement

International audienceCompton Scatter Imaging is a promising approach in imaging science. Since it employs scattered radiation that is otherwise rejected, it is claimed to improve the sensitivity of current radiation-based imaging systems. The Radon transform on V-lines models a Compton Camera and its inversion through filtered back-projection leads to an efficient way to reconstruct the density of a radiotracer. Recently, some new properties of the Radon transform on V-lines have been discovered enabling reconstruction of electronic densities in a new modality of Compton Scatter Tomography. The interest on the Radon transform on V-lines is thus renewed and novel strategies must be developed in order to fulfil the quality requirements of its applications. In this paper we study the most representative degradation effects of the Radon transform on V-lines. Particularly, we use micro local analysis to explain its artifacts and apply some strategies to compensate them

The adjoint operator of the Radon transform on rotating V-lines and its role in image reconstruction

International audienceIntegral transformations over conical sets appear as the natural mathematical models in scattered radiation imaging. Compton cameras are emblematic examples of these imaging techniques. The concept of Compton camera originates from the need to improve sensitivity in Single Photon Emission Imaging, which uses hole collimators. It advocates electronic collimation which registers radiation emitted by the radiating object and scattered by a scattering detector placed before an absorption detector. The data consists of three dimensional conical projections of the activity density of a radio-tracer. We consider here a particular two-dimensional Compton camera in which the collected data consists of the set of integrals of the density on rotating V-lines. We present approximate reconstructions obtained both from an adequate back-projection procedure, and from the action of the adjoint operator of this transform. The relation between these operators is also established

On a new two-dimensional Compton camera modality

International audienceCompton cameras have been proposed in order to increase sensitivity in conventional radiation imaging equipped with hole collimators. However, one must deal directly with three dimensional conical projections, which poses the inversion problem for integral data on cone surfaces which does not have so far an analytic solution. In an attempt to clarify this situation, we consider a new two-dimensional Compton camera in which the data are collected as integrals of the radio-tracer on broken lines, actually rotating V-lines, whose vertex is on a circular arch. In the absence of an inversion formula, we present simulation results obtained from a back-projection technique and truncated singular value decomposition