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.
