Efficient Algorithms for Inversion of Cone Beam Data for General Trajectories

奖摘要0505494，中央佛罗里达大学Alexander Katsevich标题：用于对一般轨迹的锥束数据进行倒置的高效算法摘要主要调查者(PI)计划开发实用的图像重建算法，用于在X射线源沿诸如圆弧、鞍形等轨迹移动的情况下对锥束变换进行倒置。预计新算法在理论上将是准确和有效的(即，具有过滤反投影结构)。除算法开发外，PI还计划对算法进行理论分析。与Radon变换相比，三维欧氏空间中锥束变换的反演是一个复杂的问题。人们对精确求逆算法的性质知之甚少。它们是否推广到了分布？Sobolev空间尺度下重构的稳定性是什么？在数据不完美的情况下，可能会出现哪些伪像？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(CT)的理论基础，因此本文的研究具有重要的现实意义。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。这是通过沿预定轨迹移动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。CT扫描可以使用门架或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。使用便携式C形臂进行体积可视化是非常有必要的。主要的应用是需要术中成像的图像引导介入手术，在这种手术中要避免移动病人。便携式C形臂的优点是它们可以移动到病人正在接受手术的房间里。鞍状轨迹可能对心脏成像有意义。所提出的研究的理论部分将导致对一般轨迹的锥束变换反演的更深入的理解。

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.