Image Reconstruction Algorithms for Optical Tomography with Large Data Sets Using the Radiative Transport Equation

Markel, Vadim A.宾夕法尼亚大学/ Kim， Arnold D.加利福尼亚大学- merced0615857 / 0616228使用辐射传输方程的大数据集光学断层扫描图像重建算法众所周知，现代医学成像已经彻底改变了临床医学的实践。也许不太为人所知的是，先进的数学工具在成像技术的发展中所起的关键作用。在本提案中，我们计划探索光学层析成像核心的基本数学问题。光学断层扫描（OT）是一种新兴的生物医学成像方式，它利用近红外光作为组织结构和功能的探针。OT的核心是一个不适定的非线性逆问题。我们建议在逆散射理论和辐射输运理论的基础上开发新的数学工具来解决这个问题。研究人员最近展示了使用在辐射输运方程（RTE）的扩散近似内有效的重建算法重建图像的能力。我们现在计划将这一发展扩展到需要RTE的全部功率的物理情况。研究人员率先取得的两项关键进展使我们提出的研究具有可行性和及时性。首先是建立辐射输运中逆散射问题的解析方法。第二个使能的发展是最近发现的平面波分解RTEGreen的功能。提出的研究将新数学方法的发展与算法开发和实验验证相结合。我们已经组建了一支跨学科和高度协作的研究团队，他们具有互补的技能，具有开展这项研究的独特资格。该团队由一名计算物理学家（Vadim Markel）、一名应用数学家（Arnold Kim）和一名理论光学物理学家兼医生（John Schotland）组成。本研究的智力优势在于基于新颖新颖的数学理论开发了高效的图像重建算法。宾夕法尼亚大学的一名研究生将接受图像重建的计算和分析方法的培训。作为加州大学的博士后，默塞德将接受运输理论前沿问题领域的培训。广泛的影响将包括提高光学层析成像重建图像的质量。我们期望当提出的发展得到充分实现时，它们可以显著提高光学断层扫描的临床应用。此外，尽管提出的工作集中在光学层析上，但一些结果也可能导致对随机系统（如大气和星际介质）中多次散射波的传播有更深入的了解。

Markel, Vadim A. Univ. of Pennsylvania / Kim, Arnold D. Univ. Of California-Merced0615857 / 0616228Image Reconstruction Algorithms for Optical Tomography with Large Data Sets Using the Radiative Transport EquationIt is well known that modern medical imaging has revolutionized the practiceof clinical medicine. What is perhaps less well known is the critical rolethat advanced mathematical tools have played in the development of imagingtechnologies. In this proposal, we plan to explore fundamental mathematicalproblems at the core of optical tomography. Optical tomography (OT) is anemerging biomedical imaging modality which employs near-infraredlight as probe of tissue structure and function. At the heart of OT is anill-posed nonlinear inverse problem. We propose to develop new mathematicaltools to attack this problem by building on recent progress made by theco-investigators in the areas of inverse scattering theory and radiativetransport theory. The investigators have recently demonstrated the abilityto reconstruct immages using reconstruction algorithms that are valid withinthe diffusion approximation to the radiative transport equation (RTE). Wenow plan to extend this development to physical situations in which the thefull power of the RTE is required. Two key developments pioneered by thecon-investigators makes the research we propose feasible and timely. Thefirst of these is the construction of analytical methods forthe inverse scattering problem in radiative transport. The second enablingdevelopment is the recent discovery of plane-wave decompositions for the RTEGreen's function. The proposed research integrates the development of newmathematical methods with algorithm development and experimental validation.We have assembled an interdisciplinary and highly collaborative team ofinvestigators with complementary skills who are uniquelyqualified to carry out this research. The team consists of a computationalphysicist (Vadim Markel), an applied mathematician (Arnold Kim), and atheoretical optical physicist and physician (John Schotland). The intellectual merit of the proposed research is the development ofefficient imaage reconstruction algorithms which are based on novel andoriginal mathematical theories. One graduate student at the University ofPennsylvania will be trained in computational and analytical methods ofimage reconstruction. A postdoctoral fellow at the Universityof California, Merced will be trained in the area of forward problems intransport theory. The broad impact will include improving the quality of reconstructed imagesin optical tomography. We expect that when the proposed developments arefully realized, they can significantly improve the clinical utility ofoptical tomography. Furthermore, although the proposed work is focused onoptical tomography, some of the results may also lead to a greaterunderstanding of the propagation of multiply scattered waves in randomsystems such as the atmosphere and interstellar media.