Efficient Algorithms for Inversion of Cone Beam Data for General Trajectories

获奖摘要0505494，亚历山大Katsevich，中央佛罗里达大学标题：针对一般轨迹的锥束数据反演的有效算法摘要主要研究者（PI）计划开发实用的图像重建算法，用于在X射线源沿沿着轨迹（例如圆和弧、鞍、期望新算法在理论上是精确和有效的（即，具有滤波反向投影结构）。除算法开发外，PI计划对算法进行理论分析。相对于Radon变换，三维欧氏空间中锥束变换的反演是一个复杂的问题。关于精确反演算法的性质知之甚少。它们能推广到分布吗？在Sobolev空间的尺度上重构的稳定性是什么？在非完美数据的情况下，可能的伪影是什么？这些是PI计划解决的一些问题。锥束变换是计算机层析成像的理论基础，本文的研究具有实际意义。CT的主要原理是从不同方向向患者发射锥形X射线束。这通过沿预定轨迹沿着移动X射线源来实现。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。CT扫描可以使用机架或C形臂进行。当扫描仪是便携式C形臂时，可能会出现圆弧轨迹。非常需要使用便携式C形臂进行体积可视化。主要应用于需要术中成像的图像引导介入手术，其中应避免移动患者。便携式C形臂的优点是它们可以移动到患者正在接受手术的房间中。鞍形轨迹可能是心脏成像所关注的。所提出的研究的理论部分将导致更深入地了解锥束变换反演一般轨迹。

Award abstract 0505494, Alexander Katsevich, University of Central FloridaTitle: Efficient algorithms for inversion of cone beam data for general trajectories ABSTRACTThe Principal Investigator (PI) plans to develop practical image reconstruction algorithms for inverting the cone beam transform in the cases when the x-ray source moves along trajectories, such as circle-and-arc, saddle, etc. It is expected that the new algorithms will be theoretically exact and efficient (i.e., with the Filtered Backprojection structure). In addition to algorithm development, the PI plans to perform theoretical analysis of the algorithms. As opposed to the Radon transform, inversion of the cone beam transform in the three dimensional Euclidean space is a complicated problem. Not much is known about the properties of exact inversion algorithms. Do they generalize to distributions? What is the stability of reconstruction in the scale of Sobolev spaces? What are possible artifacts in the case of non-perfect data? These are some of the questions that the PI plans to address. The proposed research is of practical significance, because the cone beam transform is a theoretical foundation of computer tomography (CT). 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 a predetermined 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. CT scans can be performed using a gantry or a C-arm. The circle-and-arc trajectory may arise when the scanner is a portable C-arm. There is a significant need for volumetric visualization using portable C-arms. The prime application is for image-guided interventional procedures requiring intraoperative imaging, in which moving the patient is to be avoided. The advantage of portable C-arms is that they can be moved into the room where the patient is undergoing the procedure. Saddle trajectories may be of interest for cardiac imaging. The theoretical component of the proposed research will result in a deeper understanding of cone beam transform inversion for general trajectories.