Program on Inverse Problems and Imaging at the Fields Institute in 2012

2012年菲尔兹研究所反问题与成像项目

• 批准号: 1240698
• 负责人: Luminita Vese
• 金额: $ 5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1240698&HistoricalAwards=false
• 关键词: Program; Inverse; Problems; Imaging; Fields

This project will support research and educational activities as part of the Thematic Program on Inverse Problems and Imaging at the Fields Institute in 2012. The organizers aim to create an environment conducive to collaborative research by combining the particiapnts' high-level expertise from Partial Differential Equations, Nonlinear Variational Methods, Differential Geometry, Regularization Theory and Numerical Analysis. Techniques initially developed in image processing or in microlocal analysis will be extended to treat novel hybrid inverse problems. Modern faster and more accurate optimization techniques for recovering data from undersampled measurements will be explored. Nonlocal methods have been recently proven to be the most efficient techniques in image denoising and image regularization. Current and future directions for solving a large range of inverse problems by nonlocal methods and their computational challenges will be studied.By integrating research and education, the organizers will introduce next generation researchers in Medical Imaging to the recent important and deep mathematical advances in the field. Numerous lectures, graduate and short courses will be given by leading researchers in the fields of inverse problems and imaging. These problems have important applications in medical imaging, geophysical prospecting and nondestructive testing. Graduate and postdoctoral students will greatly benefit from being exposed to these most active areas of research in mathematics today. They will also be exposed to interdisciplinary research mixing theoretical advances with up to date applied issues. Women and underrepresented groups will be given the opportunity to actively participate in the program as organizers, speakers, and regular participants. Teams of graduate students will be offered a summer research experience on concrete problems in medical imaging.

该项目将支持研究和教育活动，作为2012年菲尔兹研究所反问题和成像专题方案的一部分。组织者旨在通过结合参与者的偏微分方程，非线性变分方法，微分几何，正则化理论和数值分析的高水平专业知识，创造一个有利于合作研究的环境。最初在图像处理或微局部分析中开发的技术将被扩展到处理新的混合反问题。现代更快，更准确的优化技术，从欠采样测量恢复数据将被探索。近年来，非局部方法被证明是图像去噪和图像正则化中最有效的方法。通过将研究与教育相结合，组织者将向医学成像领域的下一代研究人员介绍该领域最近重要而深入的数学进展。许多讲座，研究生和短期课程将由反问题和成像领域的领先研究人员提供。这些问题在医学成像、地球物理勘探和无损检测等领域有着重要的应用。 研究生和博士后学生将大大受益于接触到这些最活跃的数学研究领域。他们还将接触到跨学科研究，将理论进步与最新的应用问题相结合。妇女和代表性不足的群体将有机会作为组织者、发言人和经常参与者积极参与该方案。研究生团队将提供一个夏季的研究经验，在医学成像的具体问题。