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，正在拯救数百万人的生命。这种技术还广泛应用于工业无损检测、地球物理、地震、天文学等领域。最近，他们发现了检测非法武器级核材料的重要应用，尽管还不是很成熟。对更新、更安全、更便宜、更强大的成像技术的追求正在进行中，并在最近几年得到加强。该项目的主旨是开发新的医学成像技术并改进一些现有技术，以及开发有效的方法来探测过境点和港口内的非法核材料。近年来，革命性的“混合/耦合物理”医学成像方法已经出现，研究人员、他的学生和他的合作者做出了重大贡献。通过组合几种不同类型的物理波，它们克服了经典技术的局限性，提供了潜在的挽救生命的诊断信息--成本更低，对患者的健康危害更小。这些模式中的图像是通过复杂的数学程序获得的，而不是通过直接获取。该项目的一部分致力于开发几种这样的新技术。另一个部分是改进最近为国土安全问题提出和开发的新技术，即在过境和港口使用的货物中检测非法武器级核材料。该项目对国土安全中几种敏感、廉价和安全的诊断医学成像新方法和高效核威胁检测新技术的开发具有重大影响，并可能在其他领域应用。研究生在这个项目中扮演着重要的角色，这为他们在精确科学、医学、生物学和国土安全的交叉领域工作做好了准备。该项目涉及核心的解析和数值问题，以及新兴耦合物理的几种新技术。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，它避免了粒子的机械准直，因此非常适合于医疗诊断中的高噪声模式，如单光子发射断层扫描。康普顿照相机及其目前开发的用于中子探测的类似物在探测低排放非法武器级放射源的存在而不是强背景噪音方面更有希望。在这里，医学成像中常用的精确重建技术不起作用，但分析和统计工具的混合进一步降低了非常低的信噪比。另一种很可能走得更远的方法是训练深层神经网络用于检测目的。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.