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

使用辐射传输方程的大数据集光学层析成像的图像重建算法

• 批准号: 0615857
• 负责人: Vadim Markel
• 金额: $ 19.9万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0615857&HistoricalAwards=false
• 关键词: Image; Reconstruction; Algorithms; Optical; Tomography

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.

Markel，Vadim A. Univ。宾夕法尼亚州 /金（Kim），阿诺德（Arnold D. Univ）众所周知，使用辐射传输方程式的大型数据集的加利福尼亚 - 梅尔森 - 麦克风0615857 /0616228图像重建算法，现代医学成像彻底改变了临床医学的实践。也许鲜为人知的是高级数学工具在成像技术的开发中发挥了关键作用。在此提案中，我们计划探索光学断层扫描核心的基本数学问题。光学断层扫描（OT）是变成生物医学成像方式，它采用近红外光作为组织结构和功能的探针。 OT的核心是Anill-Poss的非线性逆问题。我们建议开发新的数学工具来攻击这一问题，从而建立在反散射理论和辐射电视节理论领域的最新进展。研究人员最近证明了使用重建算法在扩散到辐射传输方程（RTE）内有效的重建算法的能力。 Wenow计划将这一发展扩展到需要RTE的FULLEL力量的物理情况。 Thecon Investigators开创的两个关键发展使我们提出了可行和及时的研究。首先是构建辐射运输中反向散射问题的分析方法。第二个启用开发是最近发现了RTEGREEN功能的平面波分解。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。我们已经通过互补的技能组装了一个跨学科和高度协作的团队，这些技能是独特的，以进行这项研究。该团队由一个计算理学家（Vadim Markel），一个应用的数学家（Arnold Kim）和理论的光学物理学家和医师（John Schotland）组成。拟议的研究的智力优点是基于新型的固定数学理论的有效iMaage重建算法的发展。 Pennsylvania大学的一名研究生将接受计算和分析方法的培训。默塞德（Merced）是加利福尼亚大学的博士后研究员，将在远期问题intransport理论领域接受培训。广泛的影响将包括提高光学层析成像中重建图像的质量。我们预计，当拟议的发展实现时，它们可以显着改善光学断层扫描的临床实用性。此外，尽管所提出的工作集中在横向上层造影术，但某些结果也可能导致对随机系统（例如大气和星际介质）中多散射波的传播的更大理解。