Shape Based Tomographic Inversion for Maximal Geometric Resolution

基于形状的层析成像反演以获得最大几何分辨率

• 批准号: 1347191
• 负责人: Anthony Yezzi
• 金额: $ 30万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1347191&HistoricalAwards=false
• 关键词: Shape; Based; Tomographic; Inversion; Maximal

This research involves the development of a set of computational tools for addressing problems of image formation arising in fields ranging from medical imaging and non-destructive evaluation of the manufactured components to subsurface environmental remediation and civil infrastructure monitoring. Common to these as well as many other problems is the need to characterize the internal structure of a region of space from data collected along the periphery. While common examples such as X-ray Computed Tomography or Magnetic Resonance Imaging yield high resolution images, the problems of interest in this effort are far more challenging due to complications associated with the physics of the underlying sensing technology as well as restrictions concerning where and how data can be acquired.To address these challenges, the work in this project exploits the fact that in many cases, the processing objective is the identification of specific regions of interest containing flaws or other anomalies. Through a multidisciplinary effort in engineering, mathematics, and computation, the investigators develop and study a powerful new class of innovative shaped based computational tools which combine variational Active Surface models, Level Set Methods, Boundary Element Methods, and Partial Differential Equations to detect/reconstruct geometric structures of interest directly from raw tomographic data in a general class of PDE-based tomographic modalities. This study has the potential to yield a substantial paradigm shift in extracting geometric knowledge from tomographic measurements for a diverse collection of societally important applications characterized by challenging physics and restrictive sensing scenarios. Of specific interest here are problems of geotechnical surface wave inversion, non-destructive testing, and impedance tomography for environmental monitoring.

这项研究涉及一套计算工具的开发，用于解决从医疗成像和制造组件的非破坏性评估到地下环境修复和民用基础设施监测等领域中出现的图像形成问题。 这些问题以及许多其他问题的共同之处是需要根据沿沿着收集的数据来表征空间区域的内部结构。虽然常见的例子，如X射线计算机断层扫描或磁共振成像产生高分辨率的图像，在这方面的努力感兴趣的问题是更具挑战性的，由于复杂的物理基础的传感技术，以及有关的限制，在哪里和如何可以获得数据。为了解决这些挑战，在这个项目中的工作利用的事实，在许多情况下，处理目标是识别包含缺陷或其它异常的感兴趣的特定区域。通过在工程，数学和计算多学科的努力，研究人员开发和研究一个强大的新的一类创新的形状为基础的计算工具，结合联合收割机变分活动表面模型，水平集方法，边界元方法和偏微分方程，直接从原始断层扫描数据中检测/重建感兴趣的几何结构，在一般类的PDE为基础的断层扫描模式。这项研究有可能产生一个实质性的范式转变，在提取几何知识，从断层扫描测量的社会重要的应用，其特点是具有挑战性的物理和限制性的传感场景的不同集合。这里特别感兴趣的是岩土表面波反演，非破坏性测试和环境监测阻抗层析成像的问题。