# Ingrid Daubechies

- James B. Duke 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

##### Biological Modeling

##### Computational Mathematics

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### Signals, Images & Data

Elected Member. National Academy of Engineering. February 2015

Basic Research Award. German Eduard Rhein Foundation. September 2013

Elected Member. National Academy of Sciences. September 2013

## Pages

### Selected Grants

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 2018

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 Daubechies, I. "An iteratively reweighted least squares algorithm for sparse regularization." *Contemporary Mathematics.* January 1, 2017. 391-411.
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Daubechies, I. "Foreword." January 10, 2009. xv-xvi.

Gao, T, Yapuncich, GS, Daubechies, I, Mukherjee, S, and Boyer, DM. "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)* 301.4 (April 2018): 636-658.
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Xu, J, Yang, H, and Daubechies, I. "Recursive diffeomorphism-based regression for shape functions." *SIAM Journal on Mathematical Analysis* 50.1 (January 1, 2018): 5-32.
Full Text Open Access Copy

Alaifari, R, Daubechies, I, Grohs, P, and Thakur, G. "Reconstructing Real-Valued Functions from Unsigned Coefficients with Respect to Wavelet and Other Frames." *Journal of Fourier Analysis and Applications* 23.6 (December 2017): 1480-1494.
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Cornelis, B, Yang, H, Goodfriend, A, Ocon, N, Lu, J, and Daubechies, I. "Removal of Canvas Patterns in Digital Acquisitions of Paintings." *IEEE transactions on image processing : a publication of the IEEE Signal Processing Society* 26.1 (January 2017): 160-171.
Full Text Open Access Copy

Yin, R, Gao, T, Lu, YM, and Daubechies, I. "A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets." *SIAM Journal on Imaging Sciences* 10.2 (January 2017): 711-750.
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Fodor, G, Cornelis, B, Yin, R, Dooms, A, and Daubechies, I. "Cradle Removal in X-Ray Images of Panel Paintings." *Image Processing On Line* 7 (2017): 23-42.
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Daubechies, I, Defrise, M, and Mol, CD. "Sparsity-enforcing regularisation and ISTA revisited." *Inverse Problems* 32.10 (October 1, 2016): 104001-104001.
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Wu, H-T, Lewis, GF, Davila, MI, Daubechies, I, and Porges, SW. "Optimizing Estimates of Instantaneous Heart Rate from Pulse Wave Signals with the Synchrosqueezing Transform." *Methods of information in medicine* 55.5 (October 2016): 463-472.
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O'Neal, WT, Wang, YG, Wu, H-T, Zhang, Z-M, Li, Y, Tereshchenko, LG, Estes, EH, Daubechies, I, and Soliman, EZ. "Electrocardiographic J Wave and Cardiovascular Outcomes in the General Population (from the Atherosclerosis Risk In Communities Study)." *The American journal of cardiology* 118.6 (September 2016): 811-815.
Full Text Open Access Copy

Huang, NE, Daubechies, I, and Hou, TY. "Adaptive data analysis: theory and applications." *Philosophical transactions. Series A, Mathematical, physical, and engineering sciences* 374.2065 (April 2016): 20150207-. (introduction)
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## Pages

Deligiannis, N, Mota, JFC, Cornelis, B, Rodrigues, MRD, and Daubechies, I. "Multi-Modal Dictionary Learning for Image Separation With Application in Art Investigation." February 2017. Full Text

Deligiannis, N, Mota, JFC, Cornelis, B, Rodrigues, MRD, and Daubechies, I. "X-ray image separation via coupled dictionary learning." August 3, 2016. Full Text

Yin, R, Monson, E, Honig, E, Daubechies, I, and Maggioni, M. "Object recognition in art drawings: Transfer of a neural network." May 18, 2016. Full Text

Yin, R, Dunson, D, Cornelis, B, Brown, B, Ocon, N, Daubechies, I, Yin, R, Dunson, D, Cornelis, B, Brown, B, Ocon, N, and Daubechies, I. "Digital cradle removal in X-ray images of art paintingsDigital cradle removal in X-ray images of art paintings (PublishedPublished)." January 28, 2014. Full Text

Puente, J, Boyer, DM, Gladman, JT, and Daubechies, IC. "Automated approaches to geometric morphometrics." 2013.

Rudin, C, Daubechies, I, and Schapire, RE. "On the Dynamics of Boosting." MIT Press, 2003.

Cvetković, Z, Daubechies, I, and Logan, BF. "Interpolation of bandlimited functions from quantized irregular samples." January 1, 2002. Full Text

Moayeri, N, Daubechies, I, Song, Q, and Wang, HS. "Wavelet transform image coding using trellis coded vector quantization." January 1, 1992. Full Text

In a paper recently published in the *SIAM Journal on Imaging Sciences*, Rujie Yin, Bruno Cornelis, Gabor Fodor, Noelle Ocon, David Dunson, and Ingrid Daubechies present an... read more »

Ingrid Daubechies, a prominent mathematician whose pioneering work on wavelets is the foundation for millions of consumer products, has received a $1.5 million grant from the Simons Foundation. The... read more »

Duke undergraduates know professor Ingrid Daubechies as an instructor of multivariable calculus, but beyond Duke, she has become famous for her study of wavelets, or mathematical functions with the ability to enhance image compression technology... read more »

SWIM (Summer Workshop In Mathematics) is a 9-day workshop for female rising senior high school students interested in mathematics. All students currently in their junior year of high school are eligible to apply. Participants in the workshop will... read more »

At a dinner I attended some years ago, the distinguished differential geometer Eugenio Calabi volunteered to me his tongue-in-cheek distinction between pure and applied mathematicians. A pure mathematician, when stuck on the problem under study,... read more »