Pioneer in wavelet analysis receives Simons grant

August 22, 2016  - By

Ingrid Daubechies, a prominent mathematician whose pioneering work on wavelets is the foundation for various consumer products and GNSS applications, has received a $1.5 million grant from the Simons Foundation.


Mathematician Ingrid Daubechies, whose pioneering work enabled use of wavelet analysis in a variety of fields, including GNSS. (Image: Duke Today)

Daubechies is the James B. Duke Professor of Mathematics and Electrical and Computer Engineering at Duke University in Durham, North Carolina.

The Math + X Investigator award provides research funds to professors at American and Canadian universities to encourage novel collaborations between mathematicians and researchers in another field of science or engineering.

Wavelets in GNSS. “The mathematical technique of wavelet analysis is being used in several different GNSS applications,” said GPS World’s Innovation columnist Richard Langley. In the October 2003 Innovation article “Wavelet Multiresolution Analysis,” Langley provides a general introduction to wavelet techniques:

“Wavelet analysis is an extension of Fourier analysis, the classical technique that decomposes a signal into its frequency components. However, Fourier analysis cannot determine the exact time at which a particular frequency occurred in the signal.

“Wavelet analysis, on the other hand, allows scientists and engineers to study the frequency structure of time-varying signals with unprecedented time resolution.

“In fact, a signal can be decomposed to obtain a time history of the different frequency bands making up the signal — an approach termed multiresolution analysis. Wavelet analysis can also compress data for more efficient storage and transmission, replacing the original data values with far fewer wavelet transform coefficients.”

Langley explains that to improve GPS accuracy, wavelet analysis is used to “de-noise” GPS pseudorange measurements, detect and eliminate cycle slips in GPS carrier-phase measurements, and separate biases such as multipath from high-frequency receiver noise.

Read more here.

Daubechies and Dinosaurs. “This is a tremendous honor,” Daubechies told Duke Today. She joined Duke’s faculty in 2011. “Thanks to these funds, I will be able to explore new ways to apply ideas from machine learning to adaptive signal analysis and to biological morphology.” For example, she will work with scientists to identify ways to measure fossilized teeth and bones in an effort to map evolutionary changes.

Born in Houthalen, Belgium, Daubechies studied physics at the Vrije Universiteit in Brussels, completing a doctorate in theoretical physics in 1980.  She conducted research at AT&T Bell Laboratories in New Jersey before joining Princeton University’s faculty in 1993, eventually becoming the first woman to be a tenured professor in mathematics.

In 2000, she was the first woman to receive the National Academy of Sciences Award in Mathematics. A decade later, she was the first woman elected president of the International Mathematical Union. She is a 1992 MacArthur Fellow, a 2010 Guggenheim Fellow and has been elected into the National Academy of Sciences and the National Academy of Engineering.

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