Inverse Problems For Biomedical Imaging and Homeland Security
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Computerized tomography plays a central role in biomedical imaging and is saving millions of lives. Such techniques are also extensively used in industrial non-destructive testing, geophysics, seismology, astronomy, and other areas. Lately, they have found important, albeit not yet well-developed, applications for detecting illicit weapons-grade nuclear materials. The quest for newer, safer, cheaper, and more robust imaging techniques is ongoing and has intensified in recent years. The main thrust of the project is the development of new techniques of medical imaging and improving some of the existing ones, as well as the development of efficient methods of detecting illicit nuclear materials at border crossings and in harbors. In recent years, revolutionary "hybrid/coupled-physics" methods of medical imaging have been emerging, with a major contribution by the investigator, his students, and his collaborators. By combining several different types of physical waves, they overcome limitations of classical techniques and deliver potentially life-saving diagnostic information - at a lesser cost and with less health hazards to a patient. The images in these modalities are obtained by complex mathematical procedures rather than through direct acquisition. A part of the project is devoted to development of several of such novel techniques. Another part is directed towards improving the recently suggested and development of new techniques for the homeland security problem of detecting illicit weapons-grade nuclear materials in cargo, to be used at border crossings and harbors. The project has a significant impact on the development of several new sensitive, inexpensive, and safe methods of diagnostic medical imaging and efficient novel techniques of nuclear threat detection in homeland security, with possible applications in other areas. Graduate students play a significant role in the project, which prepares them for work in the exciting area at the intersection of exact sciences, medicine, biology, and homeland security.The project takes up central analytic and numerical issues and several novel techniques of emerging coupled-physics. A significant effort is also devoted to the mathematics of Compton camera imaging, which is a promising novel technique that avoids mechanical collimation of particles and thus is well suited for high noise modalities such as Single Photon Emission Tomography in medical diagnostics. Compton cameras and their currently developed analogues for neutron detection carry even more promise for detecting the presence of low-emission illicit weapons grade radioactive sources versus a strong background noise. Here, the exact reconstruction techniques customary in medical imaging do not work, but a mixture of analytic and statistical tools goes much further down to very low signal-to-noise ratios. Another approach, which most probably can go even further, is to train deep neural networks for detection purposes.This award reflects NSF''s statutory mission and has been deemed worthy of support through evaluation using the Foundation''s intellectual merit and broader impacts review criteria.