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

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计划的一部分。组织者旨在通过结合各参与方在偏微分方程、非线性变分方法、微分几何、正则化理论和数值分析方面的高水平专业知识，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。将探索从欠采样测量中恢复数据的现代、更快、更准确的优化技术。近年来，非局部方法已被证明是图像去噪和图像正则化中最有效的方法。将研究当前和未来用非局部方法解决大量逆问题的方向及其计算挑战。通过整合研究和教育，组织者将向下一代医学成像研究人员介绍该领域最新的重要和深入的数学进展。许多讲座、研究生课程和短期课程将由反问题和成像领域的主要研究人员讲授。这些问题在医学成像、地球物理勘探、无损检测等领域有着重要的应用。研究生和博士后学生将极大地受益于今天接触到这些最活跃的数学研究领域。他们还将接触到将理论进步与最新应用问题相结合的跨学科研究。妇女和代表性不足的群体将有机会作为组织者、演讲者和定期参与者积极参与该计划。研究生团队将被提供一个关于医学成像具体问题的暑期研究经验。

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.