Collaborative Research: Direct Reconstruction Methods for Optical Tomography and Related Inverse Problems

合作研究：光学断层扫描的直接重建方法及相关反问题

• 批准号: 1108969
• 负责人: John Schotland
• 金额: $ 20万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1108969&HistoricalAwards=false
• 关键词: Collaborative; Research; Direct; Reconstruction; Methods

The objective of this proposal is to develop direct image reconstruction methods for optical tomography. Optical tomography is an emerging biomedical imaging modality that uses multiply-scattered light as a probe of tissue structure and function. The project will involve three components. (i) We will develop direct reconstruction methods, based on the inverse Born series, for recovering the absorption and diffusion coefficients of the radiative transport equation and the diffusion equation from boundary measurements. We will characterize the convergence, approximation error and stability of the proposed methods. (ii) We will develop fast reconstruction algorithms based on the inverse Born series. The algorithms will be designed to be used with data sets as large as 10^8 measurements. The algorithms will be tested using numerically simulated forward data and experimental data obtained from a noncontact optical tomography system. (iii) We will explore direct inversion methods for related inverse problems that share a common mathematical structure with optical tomography. In particular, we will develop and analyze reconstruction methods, based on inversion of the Born series, for electrical impedance tomography and for the Maxwell equations in the near-field.One of the grand challenges in biomedical imaging is to develop high-resolution methods for imaging of physiological and molecular function. The long-term goal of this research is to contribute to the solution to this problem by developing the necessary mathematical tools. The ability to detect and characterize disease at much earlier stages than is currently possible would be transformative and is critically linked to the development of robust and accurate image reconstruction algorithms for functional imaging. Two graduate students and an undergraduate will be trained to function in this interdisciplinary environment. The results of the research will be broadly disseminated and computer codes will be made publicly available for noncommercial use.

该方案的目的是开发用于光学层析成像的直接图像重建方法。光学层析成像是一种新兴的生物医学成像方式，它使用多重散射光作为组织结构和功能的探针。该项目将涉及三个组成部分。(I)我们将发展基于逆Born级数的直接重建方法，从边界测量中恢复辐射输运方程和扩散方程的吸收和扩散系数。我们将对所提出的方法的收敛、逼近误差和稳定性进行刻画。(Ii)开发基于逆Born级数的快速重建算法。这些算法将被设计用于处理最大可达10^8个尺寸的数据集。这些算法将使用数值模拟的正演数据和从非接触式光学层析成像系统获得的实验数据进行测试。(Iii)我们将探索与光学层析成像具有共同数学结构的相关逆问题的直接反演方法。特别是，我们将开发和分析基于Born级数逆的近场电阻抗断层成像和Maxwell方程的重建方法。生物医学成像中的重大挑战之一是开发用于生理和分子功能成像的高分辨率方法。这项研究的长期目标是通过开发必要的数学工具来为解决这个问题做出贡献。在比目前可能的更早的阶段检测和确定疾病的特征的能力将是变革性的，并与开发用于功能成像的稳健和准确的图像重建算法至关重要。两名研究生和一名本科生将接受培训，以便在这种跨学科的环境中发挥作用。研究结果将被广泛传播，计算机代码将公开用于非商业用途。