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

马克尔，瓦迪姆A.大学。宾夕法尼亚/金大学，阿诺德·D大学。加利福尼亚州-Merced0615857/0616228使用辐射传输方程的大数据集光学层析成像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发挥了关键作用。在这项提议中，我们计划探索光学层析成像核心的基本数学问题。光学层析成像(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。我们建议在研究人员在逆散射理论和辐射传输理论领域取得的最新进展的基础上，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)的扩散近似下有效的重建算法来重建图像的能力。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。研究人员开创的两个关键发展使我们提出的研究既可行又及时。第一个是辐射输运中逆散射问题的解析方法的构造。第二个使能发展是最近发现的RTEGreen函数的平面波分解。这项拟议的研究将新数学方法的开发与算法开发和实验验证相结合。我们组建了一支跨学科、高度协作的研究人员团队，他们具有互补的技能，唯一有资格开展这项研究。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内科医生(John Schotland)组成。所提出的研究的智力价值在于基于新颖和原创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方面的培训。作为加州大学的博士后研究员，默塞德将接受交通运输理论正问题领域的培训。广泛的影响将包括改善光学断层扫描中重建图像的质量。我们预计，当所提议的发展完全实现时，它们可以显著提高光学断层扫描的临床实用价值。此外，尽管拟议的工作主要集中在光学层析成像方面，但其中的一些结果也可能有助于更好地理解随机系统中的多次散射波的传播，如大气和星际介质。

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.