## Ingrid Daubechies

Wolf Prize Laureate in Mathematics 2023

**Ingrid Daubechies**

#### Affiliation at the time of the award:

**Duke University, USA**

#### Award citation:

**“for work in wavelet theory and applied harmonic analysis”.**

#### Prize share:

**None**

Ingrid Daubechies is a Belgian mathematician and physicist at Duke University in Durham, North Carolina. She earned her bachelor’s degree in physics from the Free University of Brussels in 1975. She then continued her research at the same university, earning her doctorate in physics with a thesis on the Representation of quantum mechanical operators by kernels on Hilbert spaces of analytic functions.

Ingrid Daubechies’ love for math and science was nurtured from a young age. Her father fostered her curiosity and interest in these subjects while she was in school. As a child, she was fascinated by how things worked and how to construct them, as well as the mechanisms behind machinery and the truth behind mathematical concepts. She would even calculate large numbers in her head when she couldn’t sleep, finding it captivating to see the numbers quickly grow.

Professor Ingrid Daubechies has made significant contributions to the field of wavelet theory. Her research has revolutionized the way images and signals are processed numerically, providing standard and flexible algorithms for data compression. This has led to a wide range of innovations in various technologies, including medical imaging, wireless communication, and even digital cinema.

The Wavelet theory, as presented by the work of Professor Daubechies, has become a crucial tool in many areas of signal and image processing. For example, it has been used to enhance and reconstruct images from the early days of the Hubble Telescope, to detect forged documents and fingerprints. In addition, wavelets are a vital component of wireless communication and are used to compress sound sequences into MP3 files.

Beyond her scientific contributions, Professor Daubechies also advocates for equal opportunities in science and math education, particularly in developing countries. As President of the International Mathematical Union, she worked to promote this cause. She is aware of the barriers women face in these fields and works to mentor young women scientists and increase representation and opportunities for them.

Daubechies’s most important contribution is her introduction in 1988 of smooth compactly supported orthonormal wavelet bases. These bases revolutionized signal processing, leading to highly efficient methods for digitizing, storing, compressing, and analyzing data, such as audio and video signals, computed tomography, and magnetic resonance imaging. The compact support of these wavelets made it possible to digitize a signal in time linearly dependent on the length of the signal. This was a critical ingredient for researchers and engineers in signal processing to be able to rapidly decompose a signal as a superposition of contributions at various scales.

In subsequent joint work with A. Cohen and J.C. Feauveau, Daubechies introduced symmetrical biorthogonal wavelet bases. These wavelet bases give up orthonormality in favor of symmetry. Such bases are much more suitable for treating the discontinuities arising at the boundaries of finite-length signals and improving image quality. Her biorthogonal wavelets became the basis for the JPEG 2000 image compression and coding system.

**Ingrid Daubechies is awarded the Wolf Prize for her work in the creation and development of wavelet theory and modern time-frequency analysis. Her discovery of smooth, compactly supported wavelets, and the development of biorthogonal wavelets transformed image and signal processing and filtering.**

**Her work is of tremendous importance in image compression, medical imaging, remote sensing, and digital photography. Daubechies has also made unparalleled contributions to developing real-world applications of harmonic analysis, introducing sophisticated image-processing techniques to fields ranging from art to evolutionary biology and beyond.**