2D and 3D Transmission Compton Scattering Imaging solved by Generalized Radon Transforms

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Compton scattering imaging is emerging as an innovative and complementary way to conventional X-ray imaging for diagnosing the anatomic structure of an object of interest. The Compton scattering, implied in 80 percent of the attenuation of a travelling photon flux, can be used to recover the electron density of the illuminated medium. Similarly to conventional tomography, the geometry of measurement gives rise to integral operators for which reconstruction techniques have to be developed. This proposal follows on from our paper [30] which established the mathematical foundations for image reconstruction of some modalities in Compton scattering tomography (CST) via the study of a family of Cormack-type Radon transforms. Nevertheless, the integral modelings proposed in the literature and unified in [30] are too much simplified to be applied in practice. The use of Compton scattered photons encounters some issues : attenuation, energy resolution and incompleteness in the data. This project intends to complete the mathematical framework given in [30] in order to overcome the physical limitations which will occur in these future imaging concepts. This complete framework will provide efficient methods to study the feasibility of an innovative CST modality. This modality, which merges the concept of the current CST ones, makes a perfect use of the scattered radiation and appears of interest for the future of imaging.Furthermore, an extension to 3D of the studied modalities could constitute the mathematical foundations for a new concept of Compton scattering imaging in 3D working by transmission. In the designed system, the revolution of a couple source/detector along the whole sphere enables the recovery of the electron density directly in 3D. This pioneering concept would be of interest in featuring a 3D object since only one detector is required and due to the high sensitive data of Compton scattering modalities. Furthermore, its application in non-destructive testing, where data acquisition time is not limited, appears especially relevant. In conclusion, the aim of the proposed project is to provide a complete mathematical framework in image reconstruction for modalities in 2D and 3D Compton imaging which will emerge in the next decade.