Novel techniques for cardiac imaging

锥束计算机层析成像(CT)是一种常见的医学成像方式。CT的主要原理是从不同方向发射一束锥形X射线穿过病人。这是通过沿某个轨迹移动x射线源来实现的。对于每个源位置，探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倒置。锥束CT的主要例子是螺旋扫描和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。在这个项目中，PI计划集中在以下三个方向：1)开发用于多源螺旋CT的准确和高效的重建算法；2)开发用于C-ARM的源轨迹的准确和高效的重建算法；以及3)开发用于动态和运动补偿CT的局部层析成像算法。拟议活动的智力优势将是为锥束CT开发新的重建算法，并更深入地理解重建扫描过程中变化的对象所涉及的数学。预计更广泛的影响将包括提高心脏成像的质量，潜在地导致用非侵入性诊断工具取代有创性诊断工具。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.