Efficient Algorithms for Inversion of Cone Beam Data for General Trajectories

一般轨迹锥束数据反演的高效算法

• 批准号: 0505494
• 负责人: Alexander Katsevich
• 金额: --
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505494&HistoricalAwards=false
• 关键词: Efficient; Algorithms; Inversion; Cone; Beam

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.

摘要：项目负责人（PI）计划开发一种实用的图像重建算法，用于x射线源沿圆弧、鞍形等轨迹运动情况下的锥形光束变换反演。预计新算法在理论上是精确和有效的（即过滤后的反向投影结构）。除了算法开发之外，PI计划对算法进行理论分析。相对于Radon变换，锥束变换在三维欧几里德空间中的反演是一个复杂的问题。人们对精确反演算法的性质知之甚少。它们能推广到分布吗？索博列夫空间尺度下重构的稳定性是什么？在非完美数据的情况下，有哪些可能的伪影？这些都是PI计划解决的一些问题。锥束变换是计算机断层扫描（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。这是通过沿着预定轨迹移动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。CT扫描可以使用龙门架或c型臂进行。当扫描仪为便携式c型臂时，可能会出现圆弧轨迹。使用便携式c型臂进行体积可视化是非常必要的。主要应用于需要术中成像的图像引导介入手术，其中避免移动患者。便携式c型臂的优点是，它们可以移动到病人正在接受手术的房间里。鞍形轨迹可能是心脏成像的兴趣点。提出的研究的理论组成部分将导致对一般轨迹的锥束变换反演有更深的理解。