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: 1108858
• 负责人: Shari Moskow
• 金额: $ 24万
• 依托单位: Drexel University
• 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=1108858&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.

本提案的目的是开发直接的图像重建方法的光学层析成像。光学层析成像是一种新兴的生物医学成像方式，它使用多次散射光作为组织结构和功能的探针。该项目将包括三个组成部分。(i)我们将开发直接重建方法，逆玻恩级数的基础上，从边界测量恢复的辐射传输方程和扩散方程的吸收和扩散系数。我们将描述所提出的方法的收敛性，逼近误差和稳定性。(ii)我们将开发基于逆玻恩级数的快速重建算法。这些算法将被设计用于多达10^8次测量的数据集。该算法将使用数值模拟的前向数据和实验数据从非接触式光学层析成像系统进行测试。(iii)我们将探讨直接反演方法的相关反问题，共享一个共同的数学结构与光学层析成像。特别是，我们将开发和分析重建方法，基于玻恩级数的反演，电阻抗断层扫描和近场的麦克斯韦方程。生物医学成像的巨大挑战之一是开发高分辨率的方法，用于生理和分子功能的成像。 这项研究的长期目标是通过开发必要的数学工具来解决这个问题。在比目前可能的更早的阶段检测和表征疾病的能力将是变革性的，并且与功能成像的稳健和准确的图像重建算法的开发密切相关。两名研究生和一名本科生将接受培训，在这个跨学科的环境中发挥作用。研究结果将广泛传播，计算机代码将公开供非商业用途。