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Analytic and Numerical Methods for Emerging Tomography Techniques

新兴断层扫描技术的分析和数值方法

基本信息

批准号：
2206279
负责人：
Fatma Terzioglu
金额：
$ 20万
依托单位：
North Carolina State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-01 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206279&HistoricalAwards=false
关键词：
Analytic Numerical Methods Emerging Tomography

项目摘要

Tomography techniques, which are used for non-invasive visualization of the interior structure of an object of interest, have transformed many fields, including astronomy, medicine, industrial non-destructive testing, homeland security, archaeology, biology, geophysics, and others. Together with technological innovations, mathematical approaches have been instrumental in advancing these techniques. The project will address mathematical problems arising from two promising tomography techniques: Multi-energy Computed Tomography (MECT) and Compton Camera Imaging (CCI). Both methods are highly useful in imaging applications. MECT is an x-ray transmission imaging method that uses the energy dependence of x-ray attenuation to determine the elemental composition of an object of interest. The conventional single-energy CT uses a simplified (linear) model for x-ray transmission, and thus, produces a grayscale image revealing only the morphology of scanned objects. In contrast, MECT can provide quantitative information and visualization in color, as a result of the more accurate modeling. MECT is regarded as a reinvention of CT imaging and is anticipated to have a significant impact on medical imaging in the coming years. Compton cameras have been used in astronomy as a telescope to detect atmospheric or cosmic gamma-ray sources. Pilot studies have shown that it can be used in a wide range of medical imaging applications, as well as radioactive decontamination. The result will also be useful in homeland security imaging for detecting illicit nuclear materials. Besides its practical benefits, the project will create opportunities for training, research experience, and career development for graduate and undergraduate students. It will also facilitate interdisciplinary collaborations.Image reconstruction in MECT requires solving a nonlinear inverse problem, for which iterative approaches must be used because an analytical solution has yet to be discovered. Although developing image reconstruction algorithms in MECT has been a very active research area, the studies systematically analyzing the uniqueness and stability of inversion have been limited. In the current practice, the scan protocol yielding unique and stable reconstructions is primarily determined by examining the noise in images obtained from physical phantom experiments. A major goal of the project is to develop a systematic approach for the design of MECT scan parameters based on the stability estimates for the MECT measurement model. A major challenge for using Compton cameras in medical applications will be overcoming the complexity of image reconstruction. The investigator will develop effective and computationally efficient image reconstruction methods for Compton cameras as well as analyses for admissible detector geometries and measurement uncertainties. Numerical techniques for the assessment of the theoretical results of the project will also be developed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

用于感兴趣对象的内部结构的非侵入性可视化的断层摄影技术已经改变了许多领域，包括天文学、医学、工业无损检测、国土安全、考古学、生物学、生物物理学等。数学方法与技术创新一起，在推进这些技术方面发挥了重要作用。该项目将解决两种有前途的断层扫描技术所产生的数学问题：多能量计算机断层扫描（MECT）和康普顿照相机成像（CCI）。这两种方法在成像应用中非常有用。MECT是一种X射线透射成像方法，其使用X射线衰减的能量依赖性来确定感兴趣对象的元素组成。传统的单能量CT使用简化的（线性）模型进行X射线传输，因此，产生的灰度图像仅显示扫描对象的形态。相比之下，MECT可以提供定量信息和可视化的颜色，作为更准确的建模的结果。MECT被认为是CT成像的再发明，预计将在未来几年对医学成像产生重大影响。康普顿照相机在天文学中被用作望远镜来探测大气或宇宙伽马射线源。初步研究表明，它可用于广泛的医学成像应用以及放射性净化。其结果也将有助于国土安全成像，以检测非法核材料。除了其实际利益，该项目将为研究生和本科生创造培训，研究经验和职业发展的机会。MECT的图像重建需要求解一个非线性逆问题，由于尚未找到解析解，因此必须使用迭代方法。虽然MECT图像重建算法的发展一直是一个非常活跃的研究领域，但系统地分析反演的唯一性和稳定性的研究还很有限。在目前的实践中，扫描协议产生独特的和稳定的重建主要是通过检查从物理体模实验获得的图像中的噪声来确定。该项目的一个主要目标是开发一个系统的方法，设计的MECT扫描参数的基础上的稳定性估计的MECT测量模型。在医疗应用中使用康普顿相机的一个主要挑战是克服图像重建的复杂性。研究人员将开发有效的和计算效率高的图像重建方法的康普顿相机，以及分析可接受的探测器的几何形状和测量不确定性。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。