Models and algorithms for three-dimensional computed tomography

计算机断层扫描 (CT) 已成为最常用的三维成像技术，主要用于医学领域，但也用于工业环境。现有技术虽然非常有用，但在特定条件下仍可能存在重大局限性（伪影、缺乏精度）。我们的目标是克服医学 CT（血管和骨科成像）特定应用以及新兴成像方式（微波断层扫描）中的这些限制。 为此，我们将重点关注CT重建方法的三大要素： 1）数据形成模型 - 我们将开发一种公式，其中几何元素（断层扫描实验期间研究介质相对于测量设备移动的方式）与物理方面（测量过程中的相互作用现象）分离。这将增加灵活性并减少计算时间，以及潜在的并行实施。 2) 优化方法和算法 - 我们将扩展之前对优化方法的比较，并研究利用它们的新方法，特别是在衍射断层扫描的困难情况下。此外，推导与数据形成模型的结构相关的适当预处理器将加速优化方法。 3) 实现 - 使用高级工具，我们将研究使用图形处理器单元的功能大规模并行实现数据形成模型中存在的几何变换的潜力。这将导致总体计算时间显着减少。 我们将通过医疗和工业领域的合作开发由此产生的方法，将为目标应用提供更准确的结果。

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.