3D Spectral Imaging based on Compton scattering: data modelling and reconstruction strategies

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In a standard CT-scan, a x-ray source irradiates a target and a set of detectors measures the attenuation of the crossing beams for various source positions. The measured data is then processed to get an image featuring the target in a non-invasive manner. In this classical scheme, the energy of the detected radiation is unexploited as a data variable. The recent development of spectral cameras opens the way for designing energy-based imaging systems. One concept consists in considering a monochromatic source and modelling the spectrum of the measured photon flux by the Compton effect. In this context, our previous project developed suitable forward models and reconstruction methods when the scattered radiation is assumed only of order one. However, the scattered radiation of order larger than one represents a substantial part of the complete spectrum. Considering higher scattering orders changes the nature of the data. This is why we speak in that respect of 3D Spectral Imaging based on Compton Scattering (CSpI). This will provide significant advances in imaging such as reducing the radiation dose received by the patient (in CT only 20% of the primary radiation is exploited), reducing the data acquisition time and delivering new insights of the object regarding standard techniques.Thus, we strive for developing a mathematical framework for imaging the 3D volume of an object of interest from spectral CSpI-data. For this purpose, the project is divided in two main approaches: The first one shall study the smoothness properties of the derived model for the multiple scattering to enable extracting the features of the sought-for quantity via filtered backprojection type algorithms. These are fast to compute and do not require prior information. In addition, our second approach includes data-driven strategies which allow more flexibility at the cost of prior information or computation times. In this context, we propose to first approximate the nonlinear data model by a linear operator and to consider the unknown part as an uncertain quantity. Methods from optimization theory could then bring a reconstruction scheme. At last, machine learning techniques could help to differentiate the multiple scattering from the first order within the spectrum. This would offer the possibility to further exploit the methods developed in previous project.In conclusion, the proposed project will provide the theoretical basis to exploit fully the multiple scattering for imaging purposes via future CSpI modalities.