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.

这项研究涉及开发一组计算工具，以解决从医学成像和对制成部分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产生的图像形成问题。 这些以及许多其他问题的共同点是需要表征沿周围收集的数据的空间区域的内部结构。尽管X射线计算机断层扫描或磁共振成像等常见的例子会产生高分辨率的图像，但由于与基础传感技术的物理相关的并发症以及有关数据的限制以及如何获取数据的限制，这项工作中感兴趣的问题更具挑战性。要解决这些挑战，该项目在许多情况下构成了其他情况。异常。 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.这项研究有可能在从层析成像测量中提取几何知识的几何知识中产生大量的范式转移，以收集以挑战物理和限制性传感情景为特征的各种社会重要应用。这里特别感兴趣的是岩土表面波反转的问题，非破坏性测试以及用于环境监测的阻抗断层扫描。