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Mathematician Refines Process for Wide Range of Uses

March 24, 2009

By Russ L. Hudson

A mathematical process, used by engineers to screen out repetitive and extraneous datacomputer-simulate new designs for things like airplane wings without having to build it, has been turned to very different uses by a Cal State Fullerton mathematician: stock market speculation, satellite imaging and cancer detection.

The process, called feature extraction, screens repetitive and extraneous data to focus only on the information relevant to a particular objective.

“I developed several feature extraction algorithms and refined them to make them more adaptive and flexible for real-time, real-world use,” said Charles Lee, associate professor of mathematics. “It can track stocks and flex with the imponderables that frequently affect them. It also can do rapid assessments of hundreds of DNA arrays to spot the genetic commonalities that can indicate certain cancers or a predilection for them, and it can quickly analyze bits of images from hundreds of antennae pointed at space even as they come in, without waiting for the entire image to load.

“As a test, a student and I spent a year tracking the stocks of more than 100 companies, two-thirds of which were losing money. With this version of feature extraction, we were able to react quickly and, if we had actually invested, we could have made money,” Lee said.

NASA and its Jet Propulsion Laboratory like Lee’s work with feature extraction. Since 2000, he has participated in research in JPL’s Flight Communications Systems Group and the Communications Research Section, including large antenna arrays.

“I was working on improving communications with space vehicles,” Lee explained. “Signal strength can vary, depending on the angle the vehicle is to the earthbound receiver, because of the amount of the atmosphere the signal has to go through. The idea was to speed communications so more time could be spent exploring and less time communicating.”

Lee has also worked on large antenna arrays. “In principle, instead of having one giant ear listen to a weak signal millions of miles away, we can have hundred of little ears listen and collaboratively understand what the spacecraft is sending.”

This is where his feature extraction algorithms can contribute, and it is the real-time and real-world practicality of the algorithms that allows the signals to be combined quickly and immediately, even when the smaller antennae are widely scattered or of different sizes.

Since 2000, Lee has been serving as a faculty researcher with NASA under their faculty part-time program. Last year, he worked on finding the optimal placements for extending the existing NASA ground stations to best support human exploration of the moon. “I was looking at where best to place them around the world for optimum reception, then the order of the expansion to help the communications coverage evolve to its fullest capacity.”

He also has worked on the communication coverage for the next-generation space shuttle, called the Crew Exploration Vehicle, where he developed algorithms to search for the best locations to build ground stations for their activities.

He is currently working on radio frequency propagation models, using the JPL-Caltech supercomputer to investigate the impacts of lunar terrain on surface-to-surface communications. Radio waves are subject to reflection, absorption and scattering, just as light waves are. For example, radio waves are affected by the daily changes in ionization of the Earth’s upper atmosphere due to the sun’s radiation.

Lee, who joined Cal State Fullerton in 1999, received his bachelor’s, master’s and doctoral degrees in applied mathematics from UC Irvine.

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