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.

马克尔宾夕法尼亚大学/ Kim，Arnold D. 0615857/0616228基于辐射输运方程的大数据量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所起的关键作用。在这个建议中，我们计划探索光学层析成像的核心基本问题。光学层析成像（Optical Tomography，OT）是一种利用近红外光作为组织结构和功能探针的新兴生物医学成像技术。OT的核心是一个不适定的非线性反问题。我们建议开发新的aproticaltools来攻击这个问题的基础上最近取得的进展，在该地区的逆散射理论和辐射输运理论的合作调查。研究人员最近已经证明了使用重建算法重建图像的能力，这些算法在辐射输运方程（RTE）的扩散近似中是有效的。我们现在计划将这一发展扩展到需要RTE全部功率的物理情况。由助理研究员开创的两个关键进展使我们提出的研究可行且及时。第一部分是建立辐射输运中逆散射问题的解析方法。第二个使发展是最近发现的平面波分解的RTE格林函数。这项研究将新的数学方法的开发与算法开发和实验验证相结合，我们组建了一个跨学科、高度合作的研究团队，他们具有互补的技能，有资格开展这项研究。该团队由一位计算物理学家（瓦迪姆·马克尔）、一位应用数学家（阿诺德·金）和一位理论光学物理学家兼医生（约翰·肖特兰）组成。该研究的智力价值在于开发了基于新颖和原始数学理论的高效图像重建算法。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。默塞德的加州大学的博士后研究员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的重建图像质量。我们希望，当提出的发展完全实现，他们可以显着提高光学断层扫描的临床应用。此外，虽然拟议的工作集中在光学层析成像，一些结果也可能导致一个更好的理解在随机系统，如大气和星际介质中的多重散射波的传播。