Ingrid Daubechies (born August 17, 1954) (approximate pronunciation "Dobe-uh-shee") is a Belgian physicist and mathematician. She is best known for her work with wavelets in image compression.

Biography

Daubechies was born in Houthalen, Belgium, as the daughter of Marcel Daubechies (a civil mining engineer) and Simonne Duran (then a homemaker, later a criminologist). Daubechies completed her undergraduate studies in physics at the Vrije Universiteit Brussel in 1975. She obtained her Ph.D. in theoretical physics in 1980, and continued her research career at that institution until 1987, rising through the ranks to positions roughly equivalent with research assistant-professor in 1981 and research associate-professor 1985.

In 1985 Daubechies met mathematician Robert Calderbank, then on a 3-month exchange visit from AT&T Bell Laboratories, New Jersey to the Brussels-based mathematics division of Philips Research; they married in 1987. Daubechies then moved to the United States, taking a position at the Murray Hill AT&T Bell Laboratories' New Jersey facility. Earlier that same year, she had made her best-known discovery: the construction of compactly supported continuous wavelets.

Since 1993, Daubechies has been a full professor at Princeton University, where she is active especially within the Program in Applied and Computational Mathematics. She was the first female full professor of Mathematics at Princeton.

Well-known results

The name Daubechies is widely associated with

• the orthogonal Daubechies wavelet
• and the biorthogonal CDF wavelet. A wavelet from this family of wavelets is now used in the JPEG 2000 standard.

She received the Louis Empain Prize for Physics in 1984, awarded once every five years to a Belgian scientist on the basis of work done before the age of 29. Between 1992 and 1997 she was a fellow of the John D. and Catherine T. MacArthur Foundation and in 1993 was elected to the American Academy of Arts and Sciences. In 1994 she received the American Mathematical Society Steele Prize for Exposition for her book Ten Lectures on Wavelets; in 1997 she was awarded the AMS Ruth Lyttle Satter prize. She was elected to the US National Academy of Arts and Sciences in 1997.

In 2000 Daubechies became the first woman to receive the National Academy of Sciences (NAS) Award in Mathematics, presented every 4 years for excellence in published mathematical research. The award honored her "for fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelets methods a practical basic tool of applied mathematics."

In January 2005, Daubechies became just the third woman since 1924 to give the Josiah Willard Gibbs Lecture sponsored by the American Mathematical Society. Her talk was on "The Interplay Between Analysis and Algorithm."

Ingrid Daubechies was the 2006 Emmy Noether Lecturer at the San Antonio Joint Mathematics Meeting. Read her profile from the AWM.

In September 2006, the Pioneer Prize from the International Council for Industrial and Applied Mathematics was awarded jointly to Ingrid Daubechies and Heinz Engl. The citation for Daubechies reads:

The ICIAM/SIAM Pioneer Prize is awarded to Ingrid Daubechies, Princeton University, Princeton, USA, for her pioneering work in applied mathematics and applications. Her work is a permanent contribution to mathematics, science and engineering and has found widespread use in image processing and time frequency analysis. Daubechies best known achievement is her construction of compactly supported wavelets in the late 1980s. Since that time she has advanced the development of biorthogonal wavelet bases. These bases are currently the most commonly used bases for data compression. Daubechies name is widely associated with the biorthogonal CDF wavelet. Wavelets from this family are currently used in JPEG 2000 for both lossless and lossy compression. Her continuing wavelet research also resulted in path-breaking work including the discovery of Wilson bases. This discovery led to the existence of cosine packet libraries of orthonormal bases and Gaussian bases. These are now standard tools in time frequency analysis and numerical solutions of partial differential equations.

The following material, reprinted here with permission, was published in The Notices of the American Mathematical Society, March 1997, Vol. 44, No. 3, 348-349 at the occasion of Daubechies receiving the 1997 Satter Prize.

Citation The Satter Prize Committee recommends that the 1997 Ruth Lyttle Satter Prize in Mathematics be awarded to Ingrid Daubechies of Princeton University for her deep and beautiful analysis of wavelets and their applications. Her work is a permanent contribution not only to mathematics but to science and engineering. Daubechies' best-known achievement is her construction of compactly supported wavelets in the late 1980s. Over the last five years she has continued their development on the theoretical level and to applications in physics and signal processing. Her continuing research has resulted in the following path-breaking developments. Her discovery with Jaffard and Journe of orthonormal Wilson bases provided the first clues to the existence of cosine packet libraries of orthonormal bases as well as Gaussian bases. These are now standard tools in time frequency analysis as well as in the numerical analysis of partial differential equations. Her work with A. Cohen on biorthogonal wavelet bases provided a more flexible approach to the use of wavelets in image compression algorithms. Biorthogonal basis functions are currently the most common wavelets used in standard compression; they are considered to be superior to orthogonal filters in, for example, fingerprint compression. While continuing to push forward wavelet analysis, Daubechies has also made important contributions in other related areas. Of particular note are her work with Klauder on path integration and her work with her student Anna Gilbert on homogenization, which has contributed to our understanding of multiscale interactions and their computations.

Brief Biographical Sketch Ingrid Daubechies received both her bachelor's and Ph.D. degrees (in 1975 and 1980) from the Free University in Brussels, Belgium. She held a research position at the Free University until 1987. From 1987 to 1994 she was a member of the technical staff at AT&T Bell Laboratories, during which time she took leaves to spend six months (in 1990) at the University of Michigan, and two years (1991-93) at Rutgers University. She is now at the mathematics department and the Program in Applied and Computational Mathematics at Princeton University.

She was awarded a Leroy P. Steele prize for exposition in 1994 for her book Ten Lectures on Wavelets. From 1992 to 1997 she was a fellow of the John D. and Catherine T. MacArthur Foundation. She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronical Engineers. She is married and has two children.

Response from Ingrid Daubechies I would like to thank the American Mathematical Society as well as the members of the Ruth Lyttle Satter Prize Committee for awarding this prize to me this year. I am particularly grateful that the citation mentions both my theoretical work and my interest in concrete applications. They are both important to me, and it is gratifying to see them both recognized. I would also like to thank my many collaborators: working with them has enriched both my mathematics and my life.

Major awards

• Louis Empain Prize for Physics (1984)
• Steele Prize for Mathematical Exposition (1994)
• Ruth Lyttle Satter Prize in Mathematics (1997)
• IEEE Information Theory Society Golden Jubilee Award for Technological Innovation (1998)
• Fellow of the Institute of Electrical and Electronics Engineers (IEEE) (1998)
• NAS Award in Mathematics (2000)
• Noether Lecturer (2006)

References

• Ingrid Daubechies: Ten Lectures on Wavelets, SIAM 1992.

External links

• "Ingrid Daubechies", Biographies of Women Mathematicians, Agnes Scott College
• Ingrid Daubechies' homepage at Princeton University

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