Inverse Problems in Industrial Applications

反问题是一个跨学科的研究领域，它是许多科学研究和工程发展的核心。在反问题中，人们感兴趣的是从测量数据中确定关于系统的定量信息。这项建议侧重于工业应用中出现的一组逆问题。这些问题不仅为数学家们提供了在重要技术发展中产生影响的机会，也为他们提供了肯定会丰富数学科学的研究方向。要研究的四个研究领域是：(I)光缆芯部轮廓的确定；(Ii)点焊的无损评估；(Iii)条形码成像和解释；(Iv)心脏电活动的成像。建议的工作包括对问题进行建模和分析。我们还将开发有效的计算策略，利用关于未知的先验信息，并将它们合并到解决方案策略中。由于这项研究计划对与PI合作的几家公司感兴趣，预计将发生一些技术转移。

Inverse problem is interdisciplinary research field that is at the heart of many scientific inquiry and engineering development. In inverse problems, one is interested in determining quantitative information about a system from measured data. This proposal focuses on a set of inverse problems that arise in industrial applications. These problems not only offer mathematicians with opportunities to make an impact in important technological development, but also research directions that are certain to enrich mathematical sciences.Four research areas to be investigated are (i) determination of core profile of an fiber optic cable, (ii) nondestructive evaluation of spot-welds, (iii) bar code imaging and interpretation, (iv) imaging the electrical activity of the heart. The proposed work involves modeling and analysis of the problem. We will also develop effective computational strategies that exploits a priori information about the unknown and incorporates them in the solution strategy. Because this research program is of interest to several of the companies with which the PI has collaborated, it is anticipated that some technology transfer will occur.