In this research effort the investigator creates mathematical concepts and numerical methods for threat detection. Chemical and biological threats pose a significant risk to our country. Early and accurate detection, characterization and warning of a chemical or biological event are critical to an effective response. Recent advances in sensor technology allows for a rapid deployment of sensors and increased flexibility and mobility in gathering surveillance data. At the same time, the diversity of environments requiring protection is on the rise. Current algorithms for threat detection are no longer able to keep up with the numerous demands and changing environments, nor are they able to fully exploit the capabilities of future sensor technology. The goal of this research effort is to develop novel mathematical concepts and computational methods that can address the new challenges we are facing in threat detection. In particular the investigator will focus on the development of efficient, robust, and scalable algorithms for hyperspectral sensing modalities and for tomographic chemical vapor detection. This research exploits recent advances in harmonic analysis, optimization, and signal processing. The mathematical tools will include sparse representations and compressive sensing, random matrix theory, geometrical functional analysis, and numerical analysis. Strong expectation for success of this project can be based on existing solid achievements by the investigator in developing advanced mathematical concepts and turning them into real-world applications.
This research activity will enable further advances and breakthroughs in the Defense and Security sector in the form of fast and efficient numerical algorithms for the detection of chemical and biological agents via stand-off sensor modalities. The proposed research is a marriage of several areas of cutting edge mathematics with state-of-the-art threat detection technology. An important part of this effort is the close collaboration of the investigator with experts in the practical aspects of threat detection. Real world data from threat detection experiments will be used in this research, both to validate the developed methods and to improve the mathematical modeling. Beyond the project's broad technological impact, it serves as a model for the kind of cross-disciplinary activity critical for research and education at the mathematics/engineering frontier. Hence this research effort helps to train graduate students in mathematics to develop and enhance skills that are crucial and urgently needed in a high-tech oriented society.
Early and accurate detection, characterization and warning of a chemical or biological threat are critical to an effective response. Recent advances in sensor technology allows for a rapid deployment of sensors and increased flexibility and mobility in gathering surveillance data. At the same time, the diversity of environments requiring protection is on the rise. Current algorithms for threat detection are no longer able to keep up with the numerous demands and changing environments, nor are they able to fully exploit the capabilities of future sensor technology. Thus there is an urgent need for new mathematical algorithms that can address these issues. In this project novel mathematical concepts and computational methods have been developed that contribute to solving the aforementioned threat detection problems. Threat detection sensors and algorithms need to be developed in an integrated manner. This requires a close cooperation between mathematicians and domain scientists. An integral part of this research effort was therefore the collaboration of the PI with experts in the practical aspects of threat detection. Real world data from threat detection experiments have been used in this research, both to validate the developed methods and to improve the mathematical modeling. Furthermore, parts of this research effort have been carried out in collaboration with Physical Sciences Inc., a company with an excellent reputation for technical expertise and innovation in the Security and Defense sector. The emphasis of this project was on the development of efficient, robust, and scalable algorithms for tomographic chemical vapor detection, target detection via array imaging, as well as x-ray crystallography and diffraction imaging. Tomographic chemical vapor cloud detection deals with the early detection of threatening chemical substances in the battlefield but also in urban areas. The challenge is that one often has only very measurements available and the positioning of the sensors may be very constrained. Such situations typically arise when sensors are mounted on moving platforms and only a few sensors can be deployed. As part of this project several algorithms have been developed that can handle these difficulties and still provide a high-resolution map of the chemical plume. In a joint effort with Physical Sciences Inc., these routines have been integrated within an actual imaging multispectral sensor framework. Target detection via antenna arrays is an essential task in various kinds of threat detection scenarios. While radar systems have been around for many decades, the development of robust, high-resolution algorithms for detecting multiple and potentially small targets in difficult environments has remained a major challenge. In this research effort, several seemingly unrelated mathematical disciplines (discrete mathematics, optimization, probability, and signal processing) have been brought together to create a highly efficient array imaging method, that provides clear theoretical design guidelines and at the same time satisfies a variety of properties that are very desirable and important from a practical viewpoint. The resulting array imaging framework has been implemented and successfully tested by radar engineers and has gained the attention of the Department of Defense. X-Ray Crystallography and Diffraction Imaging are two main diagnosis tools in chemical and biological threat detection. One major challenge in these areas comes from the fact that detectors can often times only record intensity measurements, and the information about the phase of the optical wave reaching the detector is lost. This results in the famous phase retrieval problem. Without good algorithms for recovering the phase information, x-ray crystallography and diffraction imaging cannot yield meaningful information to scientists. In this project a substantial breakthrough has been achieve in the phase retrieval problem, culminating in a groundbreaking new algorithm, called PhaseLift, which has ignited major novel developments in this area. An example of a rreconstructed image for real world data (data courtesy of Lawrence Berkeley Labs) via PhaseLift in shown in the attached figure, which depicts a collection of 50nm colloidal gold nano-particles. The image clearly provides a high resolution of the nano-particles.
