People

Professor Daubechies' primary area of research is harmonic analysis guided by problems that arise in science, engineering, and psychology. By learning about the concerns of scientists and engineers, Prof. Daubechies works to abstract the underlying mathematical problems and then solve them with analysis.

She has worked extensively on problems related to signal analysis. One of her major areas of interest in this field is the wavelet transform. Wavelets provide a mathematical representation of a complex signaling pattern from a series of simpler building blocks. To these one can add increasingly fine and increasingly localized detail, much in the same way a painter uses smaller brushes to achieve a greater degree of detail. Her work led her to construct a family of "compactly supported" wavelets known as the "Daubechies Wavelets." This has opened the door for a new system of image compression that allows for the efficient storage of an image without sacrificing detail. The JPEG2000 file format is one consequence of this work. Her book on the subject remains central to the body of work on wavelet theory. She has also dealt with the mathematics behind the conversion from analog to digital signaling. Raw analog input, such as sound, lacks the exactness afforded to digital signals, and Prof. Daubechies' research works to improve the degree of accuracy with which this conversion takes place. Recently she has spent time as well on developing new approaches to regularize various inverse problems with applications to geophysics, neuroscience, and finance.

Useful Links

• PACM Colloquium
• APC199/MAT199 — Math Alive
• MAT314 — Real Analysis
• PACM Internet Research group: this webpage contains the datasets, in various formats, used by T. Kohovanova, K. Drakakis and I.Daubechies for their paper A detailed study of the attachment startegies of new autonomous systems in the AS connectivity graph. (See paper 107 on ID's publication.)
• 3D Visualization of distances between paintings by Van Gogh and other artists: this webpage contains a movie showing a rotating 3-dimensional arrangement of 73 paintings. The paintings are arranged according to dissimilarity distances, derived from their wavelet transforms, aiming to distinguish paintings by Van Gogh from those by other painters. For more details, see the Report by the Princeton group (E. Brevdo, S. Hughes, I. Daubechies) in Proc. May 2007 1st Intl Workshop on Image Processing for Artist Identification
• The Wavelet Digest, an electronic publication edited by Michael Unser, Swiss Federal Institute of Technology Lausanne (EPFL)

After completing her studies in Belgium at the Vrije Universiteit Brussel with a Ph.D. in physics, Prof. Daubechies worked as a researcher at her alma mater. She moved to the U.S. in 1987 to work as MTS (member of technical staff) at AT&T Bell Labs. In 1991 Prof. Daubechies began teaching mathematics at Rutgers University, and three years later she made the move to Princeton to work in PACM as well as in the mathematics department.

Professor Daubechies holds a joint appointment with PACM and the department of mathematics. From 1997-2001 she served as the director of PACM. She is responsible for the direction of the mathematics part of the integrated engineering sequence available to freshmen intending to major in engineering, and she teaches an undergraduate introductory course in applied mathematics.

PACM Students advised: S. Gorkem Ozkaya, Rachel Ward, Chenwei Zhu