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Inverse Problems with Internal Data

内部数据的反问题

基本信息

批准号：
2042888
负责人：
John Schotland
金额：
$ 31.5万
依托单位：
Yale University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2042888&HistoricalAwards=false
关键词：
Inverse Problems Internal Data

项目摘要

Advances in imaging technologies such as computed tomography (CT), magnetic resonance imaging (MRI) and super resolution microscopy have transformed the practice of clinical medicine and basic biomedical research. Although the development of such technologies is well known to depend upon progress in physics and engineering, it is less well known that applied and computational mathematics has also played an essential role. This research project studies mathematical questions that arise in new medical biomedical imaging modalities in which new novel measurements play a key role. The research will study novel mathematical algorithms that will lead to improvements in optical imaging both with respect to resolution (visualizing structures at smaller scales) and computational speed. In particular, the project aims to devise robust and accurate image reconstruction algorithms that may lead to the detection and characterization of disease at much earlier stages than is currently possible. The principal investigator has research interests in applied mathematics and theoretical physics. He is also a physician. Graduate students will be trained to function in this interdisciplinary environment.The objective of this project is to investigate inverse problems with internal data that arise in biomedical optical imaging. Two classes of problems will be considered. (i) Teh PI will develop mathematically-justified methods for imaging below the diffraction limit of resolution, also known as superresolution imaging. The proposed work includes both analysis of the inverse scattering problem with internal sources and the development of reconstruction algorithms. The algorithms will be tested and characterized using data from physically realistic numerical simulations. (ii) The PI will study inverse problems that arise in acousto-optic imaging. The research will focus on the regime of coherent multiple scattering which leads to considerable mathematical simplifications compared to incoherent imaging. In particular, the PI will develop reconstruction methods for recovering the absorption and scattering coefficients of the radiative transport equation from coherent acousto-optic measurements. Finally, the role of improvements in modeling of the acousto-optic effect on image reconstruction will be investigated.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.

计算机断层扫描（CT）、磁共振成像（MRI）和超分辨率显微镜等成像技术的进步改变了临床医学和基础生物医学研究的实践。虽然众所周知，这些技术的发展依赖于物理和工程的进步，但很少有人知道应用数学和计算数学也发挥了重要作用。该研究项目研究了在新的医学生物医学成像模式中出现的数学问题，其中新的测量方法起着关键作用。该研究将研究新的数学算法，这将导致光学成像在分辨率（在较小尺度上可视化结构）和计算速度方面的改进。具体而言，该项目旨在设计稳健而准确的图像重建算法，从而在比目前可能的更早的阶段检测和表征疾病。主要研究方向为应用数学和理论物理。他也是一名医生。研究生将被训练在这个跨学科的环境中发挥作用。该项目的目的是研究生物医学光学成像中出现的内部数据的逆问题。我们将考虑两类问题。PI将开发数学上合理的方法，用于低于衍射极限分辨率的成像，也称为超分辨率成像。提出的工作包括对具有内源的逆散射问题的分析和重建算法的发展。算法将被测试和表征使用数据从物理现实的数值模拟。PI将研究声光成像中出现的反问题。研究将集中在相干多次散射的制度，导致相当大的数学简化相比，非相干成像。特别是，PI将开发从相干声光测量中恢复辐射输运方程的吸收和散射系数的重建方法。最后，我们将探讨声光效应建模的改进对图像重建的作用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。