Mathematical Sciences: RUI Inverse Problems in Thermal Imaging

959623279 Caudill/Bryan本研究项目涉及使用热方法对材料进行无损评估时出现的逆问题的研究。 重点是研究使用技术对某些对象的不可接近部分进行成像所涉及的数学，例如，边界或物体内部不可接近的部分。 当使用热方法进行腐蚀检测时，会出现这样的逆问题。 该计划包括唯一性和连续依赖问题的研究，并探讨了相关模型参数的解决方案的依赖性质。这种分析的结果作为设计反演算法，这是理论上的声音和计算效率和可靠的基础。研究人员还考虑了其他热成像问题，包括内部裂缝，分层或空隙的位置。 当人们对物理系统进行数学建模时，自然会出现逆问题。这样的系统几乎总是具有某些不容易直接测量的未知性质。 相反，人们收集更容易获得的信息，并使用数学分析来推断未知量。例如，通过测量穿过人体的X射线束的能量，可以创建身体内部的图像，这一过程称为CAT扫描。 逆问题的其他重要示例是使用MRI和PET扫描的医学成像、声学超声波图和使用电磁方法的金属部件的非破坏性评估，例如，涡流 该项目涉及的逆问题的调查时出现的一个使用热方法来检测的存在和腐蚀的程度在内部的物质对象，如飞机机翼和机身。 ***

959623279 Caudill/Bryan This research project concerns the study of inverse problems which arise in using thermal methods for the nondestructive evaluation of materials. The focus is to investigate the mathematics involved in the use of techniques for imaging inaccessible portions of some object, e.g., an inaccessible part of the boundary, or the interior of the object. Such inverse problems arise when one uses thermal methods for corrosion detection. The program includes the study of uniqueness and continuous dependence questions, and explores the nature of the dependence of solutions on relevant model parameters. The results of this analysis serve as a foundation for designing inversion algorithms which are both theoretically sound and computationally efficient and reliable. The investigators also consider other thermal imaging problems, including the location of interior cracks, delaminations, or voids. %%% Inverse problems arise naturally when one mathematically models physical systems. Such systems almost always have certain unknown properties which one cannot easily measure directly. Instead, one gathers more readily available information and uses mathematical analysis to infer something about the unknown quantities. For example, by measuring the energy of an x-ray beam passed through a human body one can create images of the interior of the body, a process known as a CAT scan. Other important examples of inverse problems are medical imaging using MRI and PET scans, acoustic sonograms, and non-destructive evaluation of metal parts using electromagnetic methods, e.g., eddy currents. This project concerns the investigation of inverse problems which arise when one uses thermal methods to detect the presence and extent of corrosion in the interior of material objects such as aircraft wings and fuselages. ***