Tomography and Microlocal Analysis

断层扫描和微局部分析

• 批准号: 1311558
• 负责人: Eric Todd Quinto
• 金额: $ 20.25万
• 依托单位: Tufts University
• 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: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311558&HistoricalAwards=false
• 关键词: Tomography; Microlocal; Analysis

The main goals of NSF grant DMS-1311558 are to use microlocal analysis and integral geometry to understand important problems in tomography and then to use this to develop and improve algorithms for those problems. Professor Quinto will develop and test algorithms for electron microscopy, X-ray tomography, and radar. Professor Quinto will adapt and test his three-dimensional electron microscope tomography (ET) algorithm with new scanning geometries (ways of obtaining the data) in ET, and he will refine the algorithm to address more aspects of the physical model. Long-term collaborators at the Royal Institute of Technology and the Karolinska Institute, Stockholm, will provide biological and realistic simulated data. Prof. Quinto will develop Sobolev seminorms that tell how strongly features in an object will show up in its tomographic data. He will use microlocal analysis to understand streak artifacts that occur in limited angle tomography and use this to develop algorithms that decrease these streaks. A large part of the PI's research in this project will involve novel methods in bistatic radar with general flight paths. He and his collaborators will develop the microlocal theory of radar for a broad range of flight paths. They will use this to find flight paths that provide better data, and he will develop and test algorithms for these flight paths.Tomography is the mathematics that images objects from indirect data including from X-ray CT scanners, electron microscopes, or radar. He will develop methods to image submicroscopic objects from electron microscopy data, the body from X-ray tomography data, and the terrain of the earth from radar data. His electron microscopy project is undertaken with biologists and mathematicians, and it has already been used to image and understand individual sub-microscopic structures. Prof. Quinto will use sophisticated mathematics to understand which features the specific data can image well and what features cannot be well-imaged. He will use this information to improve his algorithms. Professor Quinto is committed to undergraduate teaching, advising, and mentoring a broad range of students and young mathematicians, and his NSF project will directly support this through two undergraduate projects. The PI's many undergraduate research students help accomplish his research by developing algorithms and learning the underlying mathematics as they learn to become creative researchers.

NSF拨款DMS-1311558的主要目标是使用微局部分析和积分几何来理解断层扫描中的重要问题，然后使用它来开发和改进这些问题的算法。昆托教授将开发和测试电子显微镜、x射线断层扫描和雷达的算法。Quinto教授将在ET中使用新的扫描几何（获取数据的方式）来调整和测试他的三维电子显微镜断层扫描（ET）算法，他将改进算法以解决物理模型的更多方面。皇家理工学院和斯德哥尔摩卡罗林斯卡学院的长期合作伙伴将提供生物和现实的模拟数据。昆图教授将开发Sobolev semorms，用于判断物体的特征在断层扫描数据中显示的强度。他将使用微局部分析来理解在有限角度断层扫描中出现的条纹伪影，并使用它来开发减少这些条纹的算法。PI在该项目中的大部分研究将涉及具有通用飞行路径的双基地雷达的新方法。他和他的合作者将为广泛的飞行路径发展雷达的微局部理论。他们将利用这一点来找到提供更好数据的飞行路径，他将为这些飞行路径开发和测试算法。断层扫描是利用间接数据（包括x射线CT扫描仪、电子显微镜或雷达）对物体进行成像的数学。他将开发从电子显微镜数据成像亚微观物体的方法，从x射线断层扫描数据成像人体，从雷达数据成像地球地形。他的电子显微镜项目是与生物学家和数学家一起进行的，它已经被用来成像和理解单个亚微观结构。昆图教授将使用复杂的数学来理解特定数据的哪些特征可以很好地成像，哪些特征不能很好地成像。他将利用这些信息来改进他的算法。Quinto教授致力于本科教学，建议和指导广泛的学生和年轻数学家，他的NSF项目将通过两个本科项目直接支持这一点。PI的许多本科生通过开发算法和学习基础数学来帮助他完成研究，因为他们学会了成为有创造力的研究人员。