Novel techniques for cardiac imaging

锥形束计算机断层扫描（CT）是一种常见的医学成像模式。CT的主要原理是从不同方向向患者发射锥形X射线束。这是通过沿沿着某一轨迹移动X射线源来实现的。对于每个源位置，检测器测量射束离开患者时的强度。然后根据数学算法对数据进行反演。锥形束CT的主要示例是螺旋和C形臂扫描。目前，心脏成像可以说是CT面临的最重要的挑战。在数学上，这种情况下图像重建的困难来自于被扫描的对象随时间变化的事实。因此，对于每个源位置，投影数据对应于不同的对象。在本项目中，PI计划专注于以下三个方向：1）为多源螺旋CT开发精确高效的重建算法; 2）为C形臂中使用的源轨迹类型开发精确高效的重建算法; 3）为动态和运动补偿CT开发局部断层扫描算法。拟议活动的智力价值将是为锥形束CT开发新的重建算法，并加深对重建扫描期间发生变化的物体所涉及的数学的理解。预计更广泛的影响将包括提高心脏成像质量，可能导致用非侵入性诊断工具取代侵入性诊断工具。所获得的结果也可用于其他医疗应用，如核医学和强度调制放射治疗。

Cone beam computer tomography (CT) is a common medical imaging modality. The main principle of CT is based on transmitting a cone beam of x-rays through the patient from various directions. This is achieved by moving the x-ray source along some trajectory. For each source position a detector measures the intensity of the beam as it exits the patient. Then the data are inverted according to a mathematical algorithm. Prime examples of cone beam CT are helical and C-arm scanning. At present, cardiac imaging is arguably the most important challenge facing CT. Mathematically the difficulty of image reconstruction in this case comes from the fact that the object being scanned changes with time. Thus, for each source position the projection data corresponds to a different object. In this project the PI plans to concentrate on the following three directions: 1) Development of exact and efficient reconstruction algorithms for multi-source helical CT; 2) Development of exact and efficient reconstruction algorithms for the types of source trajectories used in C-arms; and 3) Development of local tomography algorithms for dynamic and motion compensated CT. The intellectual merit of the proposed activity will be the development of new reconstruction algorithms for cone beam CT and deeper understanding of the mathematics involved in reconstructing objects that change during the scan. It is expected that the broader impacts will include improved quality of cardiac imaging, potentially resulting in replacing an invasive diagnostic tool with a non-invasive one. The obtained results can also be used in other medical applications, such as nuclear medicine and Intensity-Modulated Radiation Therapy.