Collaborative Research: ATD (Algorithms for Threat Detection): Inverse Problems Methods in Chemical Threat Detection

这一建议引入了一类新的反问题，应用于反恐努力，并受到反恐努力的激励，例如在未知战场和城市地区监视和发现有害污染源。与一大类反问题的典型设置不同，该研究涉及从非常稀疏的样本和涉及偏微分方程式的约束中求逆Radon变换。这些考虑在数学分析和建模以及在设计和实施适当的计算方法方面都提出了有趣的挑战。此外，该方案还引入了新的策略，大大降低了求逆的复杂性。PI和他的合作者一直在开发的最先进的数值技术，例如在成像和压缩传感以及反问题应用中使用Bregman迭代，将是应对这些挑战的核心。这项研究对反恐工作具有直接和直接的影响，例如在未知战场和城市地区监测和发现有害污染源。一种理想的能力是从一系列传感器的被动远程测量中重建和预测违规化学和/或生物云的下落和范围。数量非常有限的固定或移动的传感器接收和记录来自包含云(羽流)的场景的红外辐射，以及来自场景中的其他元素的辐射，例如背景和中间大气。假设传感器能够分辨接收到的总辐射的光谱，并且可能知道感兴趣的化学品的光谱特征。这项研究将有助于将传感器移动到最佳位置，检测污染源的位置和内容，预测羽流的行为，并最终将此类事件造成的损害降至最低。

This proposal introduces a class of novel inverse problems with applications to, and motivated by anti-terrorism efforts, such as surveillance and discovery of harmful comtamination sources in unknown battle fields as well as urban regions. Unlike the typical settings of a large class of inverse problems, the research involves inverting Radon transforms from very sparse samples and constraints involving parttial differential equations. These considerations present interesting challenges in both mathematical analysis and modeling as well as in the design and implementation of appropriate computational methods. In addition, this proposal introduces novel strategies which greatly reduce the complexity for the inversion. State-of-the-art numerical techniques that have been in development by the PI and his collaborators, such as the use of Bregman iteration in imaging and compressed sensing and inverse problem applications will be central in meeting these challenges. This research has immediate and direct implications for anti- terrorism efforts, such as surveillance and discovery of harmful contamination sources in unknown battlefields as well as urban regions. A desired capability is to reconstruct and predict the whereabouts and the extent of an offending chemical and/or biological cloud from passive, remote measurements from an array of sensors. A very limited number of stationary or moving sensors receive and record infrared radiation from the scene containing the cloud (plume) in addition to the radiation from other elements in the scene, such as the background and intervening atmosphere. The sensors are assumed to be able to resolve the spectrum of the receivedtotal radiation and the spectral signatures of chemicals of interest may be known. This research will help to move the sensors to optimal locations, to detect the locations and contents of thesources, to predict the plumes' behavior and ultimately to minimize the damage caused by such events.