Models and algorithms for three-dimensional computed tomography

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Computed tomography (CT) has become the most used three-dimensional imaging technique primarily in medicine, but also in industrial settings. Existing techniques, though very useful, may still present significant limitations (artifacts, lack of precision) under specific conditions. Our goal is to overcome these limitations in specific applications of medical CT (vascular and orthopedic imaging) as well as in an emerging imaging modality (microwave tomography).For this purpose, we will focus on three major elements of CT reconstruction methods: 1) Data formation models - We will develop a formulation in which the geometric elements (the way in which the investigated medium moves with respect to the measurement apparatus during a tomography experiment) are decoupled from the physical aspects (the interaction phenomena underlying the measurement process). This will result in added flexibility and reduced computing time, as well as potential parallel implementation.2) Optimization methodology & algorithms - We will expand previous comparisons of optimization methods and investigate new ways of utilizing them, particularly in the difficult case of diffraction tomography. In addition, derivation of appropriate preconditioners linked with the structure of the data formation model will yield acceleration of the optimization methods.3) Implementation - Using high-level tools, we will study the potential of massively parallel implementation of the geometric transformations present in the data formation model using the power of graphics processor units. This will result in significant reduction of the overall computation time.The resulting methods, that we will develop through collaborations in the medical and industrial fields, will provide more accurate results for the targeted applications.