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

本计画系关于医学影像混合方法之数学理论与计算工具之发展。通过混合方法，我们指的是成像技术，其中具有不同基础物理的两种模态耦合在一起，以实现所涉及的每种模态单独无法实现的对比度和分辨率。该项目关注的是一类特定的混合成像模式，将超声成像与光学成像相结合，以实现非均匀介质光学特性的高分辨率成像。我们的目标是（i）开发快速和强大的图像重建算法，这些混合模式的实际使用，和（ii）培养先进的本科生，研究生和博士后研究人员在这一领域的数学和计算研究。 该项目的主要研究工作包括但不限于：（i）开发用于未知超声特性的光声层析成像（PAT）中多系数逆问题的有效反演算法;（ii）开发用于分子成像的定量荧光PAT（fPAT）和双光子PAT（TP-PAT）中逆问题的有效重建算法;（iii）对超声调制荧光光学层析成像（UMfOT）中的逆问题进行数学分析，并在相同的设置中开发稳健的图像重建策略;以及（iv）为PAT，fPAT，TP-PAT和UMfOT，部分测量。在拟议的项目中开发的数学思想，预计将提供许多类似的反系数问题的数学和数值解决方案的见解偏微分方程，出现在许多科学和技术领域。

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.