Collaborative Research: FRG: Inverse Problems in Transport Theory

合作研究：FRG：传输理论中的反问题

• 批准号: 0554097
• 负责人: Guillaume Bal
• 金额: $ 28.18万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0554097&HistoricalAwards=false
• 关键词: Collaborative; Research; FRG; Inverse; Problems

This award supports research by a group of applied and computational mathematicians and biomedical engineers who will analyze, implement, and test image reconstruction algorithms in the emerging fields of optical tomography and optical molecular imaging. These imaging techniques are based on using photons to probe tissues and deduce their optical properties and on using molecular markers, which seek out changes inside cells that are precursors for disease development, and emit radiation that is detectable outside the body. Mathematically, we will analyze linear and non-linear inverse problems in radiative transfer theory when only angularly averaged information is available at the domain boundary. We will then devise and implement robust and accurate algorithms that reconstruct optical properties of tissues and locations of source terms from practically available measurements. We will develop fast image reconstruction algorithms, based on analytic methods applicable in simple geometries, and will test them using large data sets of experimental data from a non-contact optical tomography system operated by the University of Pennsylvania group.brbrThis project brings together an interdisciplinary team of researchers at the interface of pure and applied mathematics, theoretical physics, and medicine in order to attack mathematical problems in optical imaging of biological systems. This research is at the forefront of efforts to achieve a molecular understanding of both basic biological processes and disease states. The investigators will combine their expertise in optical physics and the modeling of the propagation of light in highly-scattering media, such as biological tissue, with mathematical studies of inverse problems. The long term goal is to understand the mathematical structure of inverse problems for the so-called radiative transport equation, and to use this knowledge to develop computationally efficient methods for image reconstruction in optical tomography.

该奖项支持一组应用和计算数学家和生物医学工程师的研究，他们将在光学断层扫描和光学分子成像新兴领域分析、实施和测试图像重建算法。 这些成像技术基于使用光子探测组织并推断其光学特性，以及使用分子标记来寻找细胞内作为疾病发展前兆的变化，并发射可在体外检测到的辐射。 在数学上，当域边界仅提供角平均信息时，我们将分析辐射传输理论中的线性和非线性逆问题。然后，我们将设计并实施稳健且准确的算法，从实际可用的测量中重建组织的光学特性和源项的位置。 我们将开发基于适用于简单几何形状的分析方法的快速图像重建算法，并将使用来自宾夕法尼亚大学小组运营的非接触式光学断层扫描系统的大型实验数据集来测试它们。brbr该项目汇集了纯数学和应用数学、理论物理和医学交叉学科的研究人员团队，以解决数学问题 生物系统的光学成像。这项研究处于对基本生物过程和疾病状态进行分子理解的前沿。 研究人员将把他们在光学物理学和光在生物组织等高散射介质中传播的建模方面的专业知识与反问题的数学研究结合起来。长期目标是了解所谓的辐射传输方程反演问题的数学结构，并利用这些知识开发光学断层扫描中图像重建的计算有效方法。