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- W3125434515 abstract "Here we introduce a new forward model and imaging modality for Bragg Scattering Tomography (BST). The model we propose is based on an X-ray portal scanner with linear detector collimation, currently being developed for use in airport baggage screening. The geometry under consideration leads us to a novel two-dimensional inverse problem, where we aim to reconstruct the Bragg scattering differential cross section function from its integrals over a set of symmetric begin{document}$ C^2 $end{document} curves in the plane. The integral transform which describes the forward problem in BST is a new type of Radon transform, which we introduce and denote as the Bragg transform. We provide new injectivity results for the Bragg transform here, and describe how the conditions of our theorems can be applied to assist in the machine design of the portal scanner. Further we provide an extension of our results to begin{document}$ n $end{document} -dimensions, where a generalization of the Bragg transform is introduced. Here we aim to reconstruct a real valued function on begin{document}$ mathbb{R}^{n+1} $end{document} from its integrals over begin{document}$ n $end{document} -dimensional surfaces of revolution of begin{document}$ C^2 $end{document} curves embedded in begin{document}$ mathbb{R}^{n+1} $end{document} . Injectivity proofs are provided also for the generalized Bragg transform." @default.
- W3125434515 created "2021-02-01" @default.
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- W3125434515 date "2021-01-01" @default.
- W3125434515 modified "2023-09-25" @default.
- W3125434515 title "Bragg scattering tomography" @default.
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- W3125434515 doi "https://doi.org/10.3934/ipi.2021010" @default.
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