# Ingrid Daubechies

- James B. Duke Distinguished Professor of Mathematics and Electrical and Computer Engineering
- Professor in the Department of Mathematics
- Professor in the Department of Electrical and Computer Engineering (Joint)

### Research Areas and Keywords

##### Analysis

wavelets, inverse problems

##### Biological Modeling

shape space

##### Computational Mathematics

inverse problems

##### Geometry: Differential & Algebraic

shape space

##### Mathematical Physics

time-frequency analysis

##### Signals, Images & Data

wavelets, time-frequency analysis, art conservation

Elected Member. National Academy of Engineering. February 2015

Basic Research Award. German Eduard Rhein Foundation. September 2013

## Pages

### Selected Grants

HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation (Senior Investigator). 2019 to 2022

Simons Foundation - Math + X Investigators awarded by Simons Foundation (Principal Investigator). 2016 to 2021

New Approaches for Better Spatial Frequency Localization in 2 and 3-Dimensional Data Analysis awarded by National Science Foundation (Principal Investigator). 2015 to 2020

Structured Dictionary Models and Learning for High Resolution Images awarded by National Science Foundation (Co-Principal Investigator). 2013 to 2017

Mathematics of Low Dimensional Represenations for Design awarded by Office of Naval Research (Co-Principal Investigator). 2011 to 2016

Discovery of Empirical Components by Information Theory, Random Matrix Theory, and Computational Topology awarded by Princeton University (Principal Investigator). 2013 to 2016

Digital Removal of Cradle Artifacts from X-rays of Old Masterworks Painted on Wood Panel awarded by Samuel H. Kress Foundation (Principal Investigator). 2014 to 2015

Voronin, S., and I. Daubechies. “An iteratively reweighted least squares algorithm for sparse regularization.” *Contemporary Mathematics*, vol. 693, 2017, pp. 391–411. *Scopus*, doi:10.1090/conm/693/13941.
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Sabetsarvestani, Z., et al. “Artificial intelligence for art investigation: Meeting the challenge of separating x-ray images of the Ghent Altarpiece.” *Science Advances*, vol. 5, no. 8, Aug. 2019, p. eaaw7416. *Epmc*, doi:10.1126/sciadv.aaw7416.
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Alaifari, R., et al. “Stable Phase Retrieval in Infinite Dimensions.” *Foundations of Computational Mathematics*, vol. 19, no. 4, Aug. 2019, pp. 869–900. *Scopus*, doi:10.1007/s10208-018-9399-7.
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Shan, S., et al. “ariaDNE: A robustly implemented algorithm for Dirichlet energy of the normal.” *Methods in Ecology and Evolution*, vol. 10, no. 4, Apr. 2019, pp. 541–52. *Scopus*, doi:10.1111/2041-210X.13148.
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Zhu, W., et al. “LDMNet: Low Dimensional Manifold Regularized Neural Networks.” *Proceedings of the Ieee Computer Society Conference on Computer Vision and Pattern Recognition*, Dec. 2018, pp. 2743–51. *Scopus*, doi:10.1109/CVPR.2018.00290.
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Yin, R., and I. Daubechies. “Directional Wavelet Bases Constructions with Dyadic Quincunx Subsampling.” *Journal of Fourier Analysis and Applications*, vol. 24, no. 3, June 2018, pp. 872–907. *Scopus*, doi:10.1007/s00041-017-9540-z.
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Gao, Tingran, et al. “Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation.” *Anatomical Record (Hoboken, N.J. : 2007)*, vol. 301, no. 4, Apr. 2018, pp. 636–58. *Epmc*, doi:10.1002/ar.23700.
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Xu, J., et al. “Recursive diffeomorphism-based regression for shape functions.” *Siam Journal on Mathematical Analysis*, vol. 50, no. 1, Jan. 2018, pp. 5–32. *Scopus*, doi:10.1137/16M1097535.
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Alaifari, R., et al. “Reconstructing Real-Valued Functions from Unsigned Coefficients with Respect to Wavelet and Other Frames.” *Journal of Fourier Analysis and Applications*, vol. 23, no. 6, Dec. 2017, pp. 1480–94. *Scopus*, doi:10.1007/s00041-016-9513-7.
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Yin, R., et al. “A tale of two bases: Local-nonlocal regularization on image patches with convolution framelets.” *Siam Journal on Imaging Sciences*, vol. 10, no. 2, Jan. 2017, pp. 711–50. *Scopus*, doi:10.1137/16M1091447.
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Fodor, G., et al. “Cradle removal in X-ray images of panel paintings.” *Image Processing on Line*, vol. 7, Jan. 2017, pp. 23–42. *Scopus*, doi:10.5201/ipol.2017.174.
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## Pages

Deligiannis, Nikos, et al. “Multi-Modal Dictionary Learning for Image Separation With Application in Art Investigation.” *Ieee Transactions on Image Processing : A Publication of the Ieee Signal Processing Society*, vol. 26, no. 2, 2017, pp. 751–64. *Epmc*, doi:10.1109/tip.2016.2623484.
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Deligiannis, N., et al. “X-ray image separation via coupled dictionary learning.” *Proceedings International Conference on Image Processing, Icip*, vol. 2016-August, 2016, pp. 3533–37. *Scopus*, doi:10.1109/ICIP.2016.7533017.
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Yin, R., et al. “Object recognition in art drawings: Transfer of a neural network.” *Icassp, Ieee International Conference on Acoustics, Speech and Signal Processing Proceedings*, vol. 2016-May, 2016, pp. 2299–303. *Scopus*, doi:10.1109/ICASSP.2016.7472087.
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Yin, R., et al. “Digital cradle removal in X-ray images of art paintings.” *2014 Ieee International Conference on Image Processing, Icip 2014*, 2014, pp. 4299–303. *Scopus*, doi:10.1109/ICIP.2014.7025873.
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Bourguignon, J. P., et al. “Why STEM (science, technology, engineering and mathematics)?” *Proceeding of the International Congress of Mathematicans, Icm 2014*, vol. 1, 2014, pp. 787–97.

Puente, Jesus, et al. “Automated approaches to geometric morphometrics.” *American Journal of Physical Anthropology*, vol. 150, WILEY-BLACKWELL, 2013, pp. 226–226.

Rudin, C., et al. “On the dynamics of boosting.” *Advances in Neural Information Processing Systems*, 2004.

Cvetković, Z., et al. “Interpolation of bandlimited functions from quantized irregular samples.” *Data Compression Conference Proceedings*, vol. 2002-January, 2002, pp. 412–21. *Scopus*, doi:10.1109/DCC.2002.999981.
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Daubechies, I. “Recent results in wavelet applications.” *Proceedings of Spie the International Society for Optical Engineering*, vol. 3391, 1998, pp. 2–9. *Scopus*, doi:10.1117/12.304919.
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Moayeri, N., et al. “Wavelet transform image coding using trellis coded vector quantization.” *Icassp, Ieee International Conference on Acoustics, Speech and Signal Processing Proceedings*, vol. 4, 1992, pp. 405–08. *Scopus*, doi:10.1109/ICASSP.1992.226350.
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Duke Mathematics professor Ingrid Daubechies was one of nine to be awarded an honorary degree from Harvard University. One of the world’s leading mathematicians, a member of the National Academy of Sciences and the National Academy of Engineering, a... read more »

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