Computational Algorithms for Imaging, Design and Inverse Problems of Particle Propagation in Heterogeneous Media

异质介质中粒子传播的成像、设计和反问题的计算算法

• 批准号: 1321018
• 负责人: Kui Ren
• 金额: $ 25.96万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-15 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1321018&HistoricalAwards=false
• 关键词: Computational; Algorithms; Imaging; Design; Inverse

This project is concerned with the computational study of some imaging, optimal design and inverse problems related to systems of kinetic equations that model the propagation of particles in complex heterogeneous media. The objective is to develop fast and robust numerical algorithms by intelligently utilizing information on the structures of both the model equations and the inverse problems that we obtained through computational and mathematical studies of them, sometimes in simplified settings. Precisely, the proposed research include (i) to develop fast forward and inversion algorithms by preconditioning the computation with computationally less expensive models; (ii) to develop efficient computational strategies for uncertainty quantification and variance reduction in the imaging and inverse problems involve randomness; and (iii) to develop and validate direct non-iterative methods for imaging in extended targets in heterogeneous media. The main motivation for the study is the application of the problems in (i) optimizing the delivery of radiation therapy to caner patients; (ii) designing efficient nano-scale semiconductor devices; and (iii) imaging extended targets in highly-scattering random environments. The proposed research is expected to have long-term impacts in the practices of intensity-modulated radiation treatment planning for cancer treatment, semiconductor solar cell design for energy harvesting, and imaging in heterogeneous environment for homeland security applications. The project involves a significant education component that aims at training both undergraduate and graduate students. The ideas and techniques developed in this project will be incorporated into a graduate level class on numerical methods for imaging and inverse problems which will benefit graduates who are interested in applying advanced mathematical and computational techniques to solve real-world problems. The lecture notes for this graduate class will be made accessible to the general public through the PI's webpage hosted by the PI's institution.

该项目涉及一些与动力学方程系统相关的一些成像，最佳设计和反问题的计算研究，该系统对复杂的异质介质中粒子的传播进行了建模。目的是通过智能地利用有关模型方程的结构以及通过它们通过计算和数学研究获得的逆问题的信息来开发快速，鲁棒的数值算法，有时在简化的设置中。确切地说，拟议的研究包括（i）通过使用计算较便宜的模型对计算进行预处理来开发快速前进和反转算法； （ii）开发有效的计算策略，以减少成像和反问题的不确定性定量和差异涉及随机性； （iii）在异质介质中开发和验证在扩展目标中成像的直接非详细方法。该研究的主要动机是（i）在（i）优化向罐头患者提供放射疗法的（i）中的应用； （ii）设计有效的纳米级半导体设备； （iii）成像在高度分散的随机环境中扩展目标。预计该拟议的研究将对癌症治疗的强度调节辐射治疗计划，半导体太阳能细胞设计以及用于国土安全应用的异质环境中的成像产生长期影响。该项目涉及一个重要的教育部分，旨在培训本科生和研究生。该项目中开发的思想和技术将被纳入用于成像和反向问题的数值方法的研究生级课中，这将使有兴趣应用高级数学和计算技术的毕业生有益于解决现实世界中的问题。该研究生班的讲义将通过PI机构托管的PI网页访问。