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.

该项目与医学成像中某些混合方法的数学理论和计算工具的发展有关。通过混合方法，我们指的是成像技术，其中两种具有不同基础物理学的模式结合在一起，以实现所涉及的每种模态无法分别达到的对比度和分辨率。该项目与特定类型的混合成像方式有关，将超声成像与光学成像进行了融合，以实现异质介质光学特性的高分辨率成像。我们的目标是（i）为这些混合方式开发快速，稳健的图像重建算法，以及（ii）培训有关该领域数学和计算研究的高级本科生，研究生和博士后研究人员。 该项目的主要研究工作包括但不限于：（i）开发具有未知超声属性的光声断层扫描（PAT）中多偏反转逆问题的有效反转算法； （ii）用于开发用于定量荧光PAT（FPAT）和两光子PAT（TP-PAT）的逆问题的有效重建算法进行分子成像； （iii）对超声调制荧光光学层析成像（UMFOT）的反问题进行数学分析，并在同一环境中发展出强大的图像重建策略； （iv）为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，并通过部分测量。预期在拟议项目中开发的数学思想将提供有关许多科学和技术领域中出现的部分微分方程的数学和数值解决方案的见解。