CIF: Small: Model-based sparse X-ray CT signal processing using polychromatic measurements

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X-ray CT measurement systems are important in modern nondestructive evaluation (NDE) and medical diagnostics. Improving reconstruction accuracy and speed of data collection in these systems could have a significant impact on these broad areas. Thanks to recent computational and theoretical advances, it is now possible to design iterative reconstruction methods that incorporate accurate nonlinear physical models into sparse signal reconstructions from significantly undersampled measurements. This research aims at achieving accurate X-ray CT reconstruction from polychromatic measurements via parsimonious nonlinear signal models.The investigators develop sparse image reconstruction methods for polychromatic CT measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. This research builds on mass attenuation parametrization that leads to a simple signal model of a polychromatic X-ray CT measurement system. Since both the mass attenuation coefficient of a material and the incident spectrum of the measurement system are functions of the photon energy, photon energy can be removed from the signal model through a change of variables, leading to integral expressions of the attenuated signal strength having the Laplace kernel form. The investigators represent the incident spectrum as a function of mass attenuation and estimate it by using an appropriate basis-function expansion. A major effort focuses on developing similar simple models and corresponding algorithms for reconstructing objects consisting of multiple materials.