Inverse Problems for Biomedical Imaging and Homeland Security

计算机断层扫描在生物医学成像中发挥着核心作用，正在挽救数百万人的生命。这些技术也广泛应用于工业无损检测、地球物理、地震学、天文学和其他领域。最近，他们发现了探测非法武器级核材料的重要应用，尽管尚未得到充分开发。近年来，对更新、更安全、更便宜、更强大的成像技术的追求不断加强。该项目的主要重点是发展新的医学成像技术和改进一些现有技术，以及发展在过境点和港口探测非法核材料的有效方法。近年来，革命性的“混合/耦合物理”医学成像方法已经出现，主要贡献来自研究者、他的学生和合作者。通过结合几种不同类型的物理波，它们克服了传统技术的局限性，并以更低的成本和对患者健康危害更小的方式提供可能挽救生命的诊断信息。这些模式下的图像是通过复杂的数学程序而不是通过直接获取获得的。该项目的一部分致力于开发几种这样的新技术。另一部分用于改进最近建议和发展的新技术，以解决国土安全问题，即探测将在过境点和港口使用的货物中的非法武器级核材料。该项目对开发几种新的敏感、廉价和安全的医学诊断成像方法和国土安全领域有效的新型核威胁检测技术具有重大影响，并可能应用于其他领域。研究生在该项目中发挥着重要作用，为他们在精确科学、医学、生物学和国土安全交叉的令人兴奋的领域工作做好准备。该项目涉及中心的解析和数值问题以及新兴的耦合物理的一些新技术。康普顿相机成像的数学也投入了大量的努力，这是一种很有前途的新技术，避免了粒子的机械准直，因此非常适合高噪声模式，如医学诊断中的单光子发射断层扫描。康普顿相机及其目前开发的中子探测类似物在检测低排放非法武器级放射源与强背景噪声的存在方面更有希望。在这里，医学成像中常用的精确重建技术不起作用，但是分析和统计工具的混合可以进一步降低到非常低的信噪比。另一种可能更深入的方法是训练用于检测目的的深度神经网络。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.