Interdisciplinary Workshop on Electromagnetic Inverse Problems

使用低频电流的成像方法广泛应用于科学和工程领域，包括医疗应用，如监测重症监护病人的通风，定位地下污染柱，勘探油藏和监测工厂中化学品的混合。使用线圈系统的类似方法也被用于寻找飞机部件的裂缝，检测飞机乘客身上的刀具，以及定位地下物体，如地雷。赞比西河和亚马逊河中的某些弱电鱼类会产生电场，以便在黑暗中或浑浊的水中探测猎物和敌人。数学家们致力于寻找从电子数据中形成图像的新方法，并了解特定测量系统的能力。这些对上面列出的应用程序感兴趣的社区很少（如果有的话）开会互相学习。由于应用领域如此不同，这是可以理解的：但是所有的应用程序都共享一个共同的数学框架，因此数学家自然应该提供会议场所。本提案的主要目的是组织一个研讨会，邀请来自上述一些主要领域的主要演讲者，以及相关数学领域的专家，在医学电成像界的主要年度会议的背景下。此外，还将安排一个较小的会议：一个代码测试，在这个代码测试中，实现最新数学图像重建方法的计算机程序将被共享并调整以协同工作。这些程序和共享数据将免费提供给在任何应用领域工作的人。

Imaging methods using low-frequency electric current are used across a wide range of science and engineering including medical applications such as monitoring ventilation of intensive care patients, locating pollution plumes underground, exploring oil reservoirs and monitoring mixing of chemicals in factories. Similar methods using systems of coils are also used to find cracks in aircraft parts, detect knives on air passengers and to locate objects, such as landmines, underground.Certain species of weakly electric fish in the Zambezi and Amazon rivers generate electric fields to detect their prey and enemies in the dark, or in cloudy water.Mathematicians work on finding new methods to form images from the electrical data, and to understand the capabilities of particular measurement systems.These communities interested in the above listed applications rarely, if ever, meet to learn from each other. As the application areas are so different this is understandable: but all applications share a common mathematical framework so it is natural that mathematicians should provide the meeting ground. The main purpose of this proposal is to organize a workshop inviting key speakers from some of the above mentioned main areas, together with experts in the relevant mathematics, in the context of the main annual meeting of the medical electrical imaging community.In addition, a smaller meeting will be arranged: a codefest in which computer programs that implement the latest mathematical image reconstruction methods, are shared and adjusted to work together. These programs together with shared data will be available freely to those working in any of the application areas.