NSF Grant Funds Math For National Security

Applying mathematics to detect chemical weapons, hidden explosives or other threats is the goal of an ongoing project at the UC Davis Department of Mathematics, supported by grants from the National Science Foundation.

Resolving blurred image with math

Blind deconvolution is a mathematical method to clarify a blurred image without knowledge of the original image, or how it was blurred. Top, original image; bottom, blurred image after blind deconvolution (Original image by Steve Byland).

Threat detection involves math at a range of levels, said Professor Thomas Strohmer, who leads the project. It can include quickly processing large amounts of data, coordinating multiple sensors, or extracting clarity from background noise.

For example, to detect poison gas on a battlefield, you might deploy sensors either on the ground with your troops or on aircraft overhead. To translate the data from those sensors into a “heat map” that tells you if a toxic gas is present, how much and exactly where it is, you need a set of algorithms.

Hyperspectral Imaging and Blind Deconvolution

One potential tool for detecting chemical threats is hyperspectral imaging. While a conventional camera uses three colors of light that can be mixed to produce the rest of the spectrum, a hyperspectral camera measures many different wavelengths of light, under ideal conditions generating a distinct signature for different chemical compounds.

A hyperspectral camera mounted on an airplane, though, is operating under less than ideal conditions. It would be collecting a lot of data with a lot of “noise,” and if the goal is to quickly pinpoint a chemical threat, the data would need to be processed very quickly.

“It’s very challenging from a mathematical point of view,” Strohmer said. “Something could look different under different environmental conditions.”

One way to deal with the “big data” problem is “compressive sensing,” a mathematical technique that focuses in on the most relevant pieces of data. Another is “deconvolution,” or using math to clarify blurred images. “Blind deconvolution” is a set of methods for resolving a blurry image, without prior knowledge of the original object.

Finally, smart algorithms can be used to automatically calibrate devices to get the best possible images.

Terahertz Imager

Strohmer is also collaborating with Professor Kubilay Sertel and other engineering faculty at the Department of Electrical and Computer Engineering at The Ohio State University who have developed an imaging device working with wavelengths between microwaves and X-rays.

These “Terahertz imagers” can “see” through clothing and just under the skin, and could be used to replace existing scanners in airports as well as for medical applications. Strohmer is developing the algorithms necessary to create images from Terahertz data.

Strohmer’s work has also received support from the U.S. Department of Defense, AFOSR, ARO, and DARPA.

More information

HELIOS Laboratory at The Ohio State University



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