Novel techniques for cardiac imaging

锥束计算机断层扫描（CT）是一种常用的医学成像方式。CT的主要原理是将一束锥形的x射线从不同的方向穿透病人。这是通过沿着某些轨迹移动x射线源来实现的。对于每个光源位置，探测器测量光束离开病人时的强度。然后根据数学算法对数据进行倒排。锥形束CT的主要例子是螺旋和c臂扫描。目前，心脏成像可以说是CT面临的最重要的挑战。从数学上讲，这种情况下图像重建的难度来自于被扫描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计划集中在以下三个方向：1)开发精确高效的多源螺旋CT重建算法；2)针对c型臂中使用的源轨迹类型，开发了精确高效的重建算法；3)动态和运动补偿CT局部断层扫描算法的发展。所提出的活动的智力价值将是锥束CT的新重建算法的发展，以及对重建扫描过程中变化的对象所涉及的数学的更深入理解。预计更广泛的影响将包括提高心脏成像的质量，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学应用，如核医学和调强放射治疗。

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.