This proposal concerns the development and evaluation of new mathematical algorithms for the detection and classification of chemical and biological agents. An automatic detection and classification system operates by first identifying the existence of a signal of interest followed by classification of the signal. The classification stage consists of comparing the observation of interest to a small library of spectra of materials of interest. There are a host of significant challenges, both logistical and technical, surrounding such automatic detection and classification of threat agents in the field. The actual spectra collected in the field may have signatures which are not a direct match to the Raman spectrum collected under controlled conditions and the amplitude of the signal of interest is generally much smaller than the amplitude of the continuously changing background spectra. New mathematical algorithms will be developed for characterizing spectral signatures using an integrated geometric and statistical approach.
The results of this research program are intended to be employed in mobile field-operable systems for the laser interrogation of surface agents (LISA) to enabled real time sensing and characterization of potential civilian and military exposure biological and chemical agents. As an example, a portable Mini-Raman Lidar System (MRLS) has been developed capable of measuring Raman spectral signatures at short standoff distances, e.g., 1-2.5 meters. These systems may be mounted on vehicles and could be used to support military operations by detecting toxic fingerprints and alerting military personnel to potential threats from chemical or biological weapons. This new technology has created the need to produce an automated biological and chemical threat agent detection system based on exploiting the characteristic signatures of Raman spectra associated with different compounds including warfare agents. The main objective of the proposed investigation is to develop algorithms capable of agent identification with a false positive rate of less than one in 90,000. This project will train two graduate students in an area of mathematics that has applications to National Security.
The primary goal of the research supported by this investigation concerns the development and evaluation of new mathematical algorithms for the detection and classifcation of chemical and biological agents in hyperspectral imagery. Our approach is geometric in the sense that we seek to characterize the shape of the data as well as its complexity, i.e., how many parameters does it take to describe the data. Our focus centered on the development of geometric tools for characterizing the geometric structure in data. We implemented and tested these tools for the detection of threat agents in hyperspectral image data sets Typical digital cameras collect light in the red, green and blue bands forming a three dimensional color space for capturing images. Hyperspectral cameras can capture many more bands that allow us to see objects in the ultraviolet and infrared as well as the visual spectrum with much higher fidelity than a standard red, green, blue camera. The direct mathematical representation of such data is a set of numbers for each location in the image. Three numbers in the case of red, green, and blue images, or say 220 numbers per location, or pixel, for a hyperspectral Airborn Visible Infrared Imaging Spectrometer (AVIRIS) image. Hyperspectral images contain a wealth of information about the physical environment. One can think of each pixel of imaging spectrometer data as a probe across the spectrum of reflected light that captures a wealth of information about the chemical or biological composition of the scene. When chemical or biological agents are released into the atmosphere, either accidently or by design, they may be detected in these hyperspectral images. The difficulty with such detections is that the environment also contains obfuscating structures, either natural or human-made, in addition to the inherent noise processes in any enviroment. We developed a range of algorithms for the threat detection application. One family of methods is rooted in the mathematical idea of a subspace representation. Typically, algorithms are applied to single pixels that serve as points. In this setting comparing two points may be achieved by measuring the standard distance while averaging points also uses the usual definition. In our geometric framework we provide a representation for a set of points in terms of a subspace. We developed new mechanisms for computing distances between such points as well as for averaging such points. These algorithms provided the core of the tools for classification and detection of threats in hyperspectral images. We have demonstrated that in many cases the algorithms developed produce state-of-the-art results in detection and classification. Another family of algorithms that we have developed deals with the sparse representation of models. We explored modifying objective functions to include terms that force model parameters to zero and showed that the resulting representations had performance enhancements. The algorithms developed for analyzing threats in hyperspectral images developed by this work have also found application in other areas. In particular, we have used the methodology to provide new diagnostic tools for neonatal and pediatric sepsis. Further, we have adapted another algorithm to identify discriminatory gene pathways for characterizing the human immune system's response to influenza. Four Masters Theses were mentored and two Ph.D. dissertations were advised during the course of this work. The graduating students have found jobs in academia that allow them to continue to disseminate the knowledge gained under this award.
