Mathematical Sciences: RUI Inverse Problems in Thermal Imaging

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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. ***