NSF/CBMS Regional Conference in Mathematical Sciences - Imaging in Random Media - Spring 2008

本次会议的目标是向面向数学的受众介绍杂乱介质中的传感器阵列成像。这是应用数学中一个新兴的交叉学科领域，起源于波传播、随机介质、统计学、最优化和数值分析。多年来，我们部署超大型传感器阵列和收集大型数据集的能力稳步提高，但现有的成像方法正在达到其极限。它的基础必须在跨学科的框架下重新审视，分辨率极限必须重新评估，对噪声和杂波的稳健性必须解决。近年来出现了一些非常有趣的结果：针对杂波介质的新的自适应成像算法已经被开发出来，并被置于一个清晰的数学框架中。提出了分辨率理论的新方法，如成像过程的统计稳定性概念和由杂波引起的分辨率损失的量化。利用统计学、随机介质中的波传播和现代最优化等工具，获得了新的图像增强技术。该会议的首席讲师乔治·C·帕帕尼科拉教授一直站在这项研究的前沿。他的演讲将向来自学术界、石油行业和医学成像的数学家介绍成像科学中一种新的数学先进技术。这项技术在地震勘探、超声波、老化混凝土结构的无损检测、树叶或探地雷达等关键应用中具有潜在的重大影响。

The goal of this conference is to introduce a mathematically oriented audience to sensor array imaging in cluttered media. This is an emerging interdisciplinary area in applied mathematics, with roots in wave propagation, random media, statistics, optimization and numerical analysis. Over the years, our ability to deploy very large sensor arrays and to collect large data sets has increased steadily, but the available imaging methodology is reaching its limits. Its foundations must be reexamined in an interdisciplinary framework, its resolution limits must be reassessed and the robustness to noise and clutter has to be addressed.Some very interesting results have emerged in recent years: Novel adaptive imaging algorithms for cluttered media have been developed and put in a clear mathematical framework. New approaches to resolution theory, such as the concept of statistical stability of the imaging process and quantification of resolution loss caused by clutter have been advanced. Novel image enhancement-techniques have been obtained using tools from statistics, wave propagation in random media and modern optimization. The principal lecturer of theconference, Professor George C. Papanicolaou, has been at the forefront of this research. His lectures will introduce mathematicians from academia, the oil industry and medical imaging to a new and mathematically advanced technology in imaging science. This is a technology with potential for a big impact in crucial applications such as seismic exploration, ultrasonic, non-destructive testing of aging concrete structures, foliage or ground penetrating radar, etc.