Collaborative research: Mathematics of emerging imaging methods in medicine and homeland security

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Computerized tomography plays a central role in biomedical imaging. Tomography techniques are also extensively used for industrial non-destructive testing, in geology and geophysics, astronomy, and in other areas. Lately, they have found important applications in homeland security. Over the last decades, several modalities have been developed and have became standard. Such are, for instance, the traditional X-ray CT scan, SPECT, MRI, Optical-, Ultrasound-, and Electrical Impedance Tomography, to name a few. However, such tasks as detection of small cancerous tumors in soft tissues or finding a small amount of nuclear material in a large container still present a significant challenge. In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have been emerging. By combining two or three different types of waves (or physical fields) these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information - at a lesser cost and with less health hazard to a patient. As a rule, the images in these modalities are obtained by complex mathematical procedures, rather than through direct acquisition. The corresponding mathematics is, mostly, at very early stages of development. Thus, the first part of the project addresses the central mathematical and numerical issues in several of the novel hybrid techniques, based on combinations of magnetic, electric, acoustic, and optical waves, and the general mathematical issues common to all of these techniques. The second part of the projects is directed toward the improvement of the known methods and development of new tomographic techniques for homeland security problems. In particular, we will focus on the detection techniques for illicit weapons-grade nuclear materials in cargo, to be used at border crossings and harbors. In the third part these techniques will be used to resolve some outstanding problems in Synthetic Aperture Radar applications, radio tomography, ultrasound reflectometry, and other areas.The goal of the project is to develop new techniques of medical imaging, as well as efficient methods of detecting illicit nuclear materials at border crossings and in harbors. The project will have a significant impact on the development and implementation of several new sensitive, inexpensive, and safe methods of biomedical imaging, efficient techniques of nuclear threat detection in homeland security, with applications in several other areas of imaging and non-destructive industrial testing (e.g., synthetic aperture radar). The results will be disseminated through publications in high quality research journals, presentations at national and international conferences, and series of lectures at various venues. Graduate students will play a significant role in the project, which will prepare them for work in the exciting area at the junction of exact sciences, medicine, biology, and homeland security. Parts of the study resulted from the project will be delivered in graduate level classes, lecture series at national and international schools and conferences, and in two monographs.