Hybrid Imaging with Acoustic and Optics: Efficient Computation via Constructive Analysis

声学和光学混合成像：通过构造性分析进行高效计算

• 批准号: 1620473
• 负责人: Kui Ren
• 金额: $ 23.9万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620473&HistoricalAwards=false
• 关键词: Hybrid; Imaging; Acoustic; Optics; Efficient

This project is concerned with the development of mathematical theory and computational tools for some hybrid methods in medical imaging. By hybrid methods we refer to imaging techniques where two modalities with distinct underlying physics are coupled together to achieve the contrast and resolution not attainable separately by each of the modalities involved. This project is concerned with a specific class of hybrid imaging modalities that couple ultrasound imaging with optical imaging to achieve high-resolution imaging of optical properties of heterogeneous media. Our objectives are (i) to develop fast and robust image reconstruction algorithms for these hybrid modalities for practical use, and (ii) to train advanced undergraduate students, graduate students, and postdoctoral researchers on the mathematical and computational research in this field. The main proposed research efforts in this project include, but not limited to: (i) to develop efficient inversion algorithms for multi-coefficient inverse problems in photoacoustic tomography (PAT) with unknown ultrasound properties; (ii) to develop efficient reconstruction algorithms for inverse problems in quantitative fluorescence PAT (fPAT) and two-photon PAT (TP-PAT) for molecular imaging; (iii) to perform mathematical analysis on inverse problems in ultrasound-modulated fluorescence optical tomography (UMfOT) and to develop robust image reconstruction strategies in the same setting; and (iv) to develop fast algorithms for the transport equation for optimization-based iterative image reconstruction strategies for PAT, fPAT, TP-PAT and UMfOT with partial measurements. The mathematical ideas developed in the proposed projects are expected to provide insights on the mathematical and numerical solutions of many similar inverse coefficient problems to partial differential equations that appear in many fields of science and technology.

该项目涉及医学成像中一些混合方法的数学理论和计算工具的发展。在混合方法中，我们指的是成像技术，其中具有不同基础物理的两种模式耦合在一起，以获得所涉及的每一种模式无法单独获得的对比度和分辨率。该项目涉及一类特定的混合成像模式，该模式将超声成像与光学成像相结合，以实现对非均匀介质光学属性的高分辨率成像。我们的目标是(I)为这些混合模式开发快速和健壮的图像重建算法以供实际使用，(Ii)培训高级本科生、研究生和博士后研究人员在这一领域的数学和计算研究。本项目的主要研究工作包括但不限于：(I)开发超声性质未知的光声层析成像(PAT)多系数反问题的高效反演算法；(Ii)开发用于分子成像的定量荧光PAT(FPAT)和双光子PAT(Tp-PAT)反问题的高效重建算法；(Iii)对超声调制荧光光学层析成像(UMfOT)反问题进行数学分析，并在相同的背景下开发稳健的图像重建策略；以及(Iv)针对PAT、fPAT、TP-PAT和UMfOT的基于优化的迭代图像重建策略，开发传输方程的快速算法。在拟议的项目中形成的数学思想有望为许多科学和技术领域出现的偏微分方程的许多类似的反系数问题的数学和数值解提供见解。