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、地球物理学、地震学、天文学和其他领域。最近，他们发现了一些重要的应用程序，尽管尚未得到很好的开发，用于检测非法武器级核材料。对更新、更安全、更便宜和更强大的成像技术的追求正在进行中，并且近年来有所加强。该项目的主旨是开发新的医学成像技术和改进某些现有技术，以及开发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，研究者，他的学生和他的合作者做出了重大贡献。通过结合几种不同类型的物理波，它们克服了经典技术的局限性，并以更低的成本和更少的健康危害提供了可能挽救生命的诊断信息。这些模式中的图像是通过复杂的数学程序而不是通过直接采集来获得的。该项目的一部分致力于开发几种这种新技术。另一部分旨在改进最近提出的关于在过境点和港口检测货物中非法武器级核材料的国土安全问题的新技术，并为此开发新技术。该项目对开发几种新的敏感，廉价和安全的诊断医学成像方法以及国土安全中核威胁检测的有效新技术产生了重大影响，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，该项目为他们在精确科学，医学，生物学和国土安全交叉的令人兴奋的领域工作做好了准备。该项目涉及中心分析和数值问题以及新兴耦合物理学的几种新技术。一个显着的努力也致力于康普顿照相机成像，这是一个有前途的新技术，避免了机械准直的粒子，因此非常适合于高噪声模态，如单光子发射断层扫描在医疗诊断的数学。康普顿照相机及其目前开发的中子探测类似物在探测低排放非法武器级放射源方面比在强背景噪声方面更有希望。在这里，医学成像中常用的精确重建技术不起作用，而是分析和统计工具的混合物进一步降低到非常低的信噪比。另一种可能更进一步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NSF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而被认为值得支持。

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.