Ingrid Daubechies | Academic Influence

Why Is Ingrid Daubechies Influential?

By Erik J. Larson, PhD

Areas of Specialization: Wavelets, Inverse Problems, Shape Space, Time-Frequency Analysis
Daubechies is the James B. Duke Professor of Mathematics at Duke University. Prior to Duke, Daubechies was William R. Kenan Jr. Professor of Mathematics at Princeton University from 2004-2011. She was the first female full professor of mathematics at the Ivy League institution. Daubechies is one of the most widely cited mathematicians, and is world renowned for her work on the mathematics of image compression, known as wavelets (an area of relevance to computer science and other disciplines in addition to mathematics). From Belgium, Daubechies received her bachelor’s in physics at the Vrije Universiteit Brussel in 1975. She received her Ph.D. from CNRS Center for Theoretical Physics in Marseille, France in 1980.

Daubechies proved an important result in wavelet theory that extended the theory to digital signal processing, a result of significant theoretic and practical significance. Her work on wavelets has made her one of the most influential mathematicians of our era. Notably, Daubechies has also been active in encouraging women to pursue studies and careers in mathematics and other cognate fields (like physics). She is co-founder of the Duke Summer Workshop in Mathematics for promising female students.

Daubechies was awarded the MacArthur Fellowship for her pivotal work in mathematics, and was elected to the American Academy of Arts and Sciences in 1993. She received the Steele Prize for Exposition for her book Ten Lectures on Wavelets in 1994. She was also the first female president of the International Mathematical Union, among other notable distinctions.

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According to Wikipedia, Baroness Ingrid Daubechies is a Belgian physicist and mathematician. She is best known for her work with wavelets in image compression. Daubechies is recognized for her study of the mathematical methods that enhance image-compression technology. She is a member of the National Academy of Engineering, the National Academy of Sciences and the American Academy of Arts and Sciences. She is a 1992 MacArthur Fellow. She also served on the Mathematical Sciences jury for the Infosys Prize from 2011 to 2013.

Ingrid Daubechies's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Ten Lectures on Wavelets (15284)
Orthonormal bases of compactly supported wavelets (8695)
The wavelet transform, time-frequency localization and signal analysis (6156)
An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint (4219)
Image coding using wavelet transform (4025)
Ten Lectures on Wavelets. (3395)
Biorthogonal bases of compactly supported wavelets (2922)
Factoring wavelet transforms into lifting steps (1706)
PAINLESS NONORTHOGONAL EXPANSIONS (1398)
Wavelet Transforms That Map Integers to Integers (1310)
Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool (1192)
Iteratively reweighted least squares minimization for sparse recovery (1105)
Wavelets on the Interval and Fast Wavelet Transforms (1100)
Factoring wavelet transforms into lifting steps (1066)
Ten Lectures on Wavelets (1037)
Framelets: MRA-based constructions of wavelet frames☆☆☆ (753)
Time-frequency localization operators: A geometric phase space approach (579)
Two-scale difference equations II. local regularity, infinite products of matrices and fractals (484)
Sparse and stable Markowitz portfolios (469)
Data Compression and Harmonic Analysis (459)
Orthonormal bases of compactly supported wavelets II: variations on a theme (440)
Two-scale difference equations I: existence and global regularity of solutions (407)
Sets of Matrices All Infinite Products of Which Converge (382)
Lossless image compression using integer to integer wavelet transforms (346)
Non-separable bidimensional wavelets bases. (288)
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints (275)
Image processing for artist identification (259)
Multiresolution analysis, wavelets and fast algorithms on an interval (233)
A simple Wilson orthonormal basis with exponential decay (232)
Independent component analysis for brain fMRI does not select for independence (222)
Gabor Time-Frequency Lattices and the Wexler-Raz Identity (196)
A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models (186)
Where do wavelets come from? A personal point of view (183)
Frames in the Bargmann Space of Entire Functions (182)
Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order (182)
Tree Approximation and Optimal Encoding (175)
Image coding using vector quantization in the wavelet transform domain (168)
A STABILITY CRITERION FOR BIORTHOGONAL WAVELET BASES AND THEIR RELATED SUBBAND CODING SCHEME (159)
Tomographic inversion using L1-norm regularization of wavelet coefficients (157)
Harmonic analysis of the space BV. (154)
Algorithms to automatically quantify the geometric similarity of anatomical surfaces (154)
Wavelets on irregular point sets (144)
On the importance of combining wavelet-based nonlinear approximation with coding strategies (143)
Time-frequency localisation operators-a geometric phase space approach: II. The use of dilations (135)
Regularity of refinable function vectors (135)
Iteratively solving linear inverse problems under general convex constraints (133)
A new technique to estimate the regularity of refinable functions (126)
Comparing Dirichlet normal surface energy of tooth crowns, a new technique of molar shape quantification for dietary inference, with previous methods in isolation and in combination. (120)
ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform (108)
An uncertainty principle for fermions with generalized kinetic energy (107)
The Dynamics of AdaBoost: Cyclic Behavior and Convergence of Margins (107)
On the approximation power of convolution-based least squares versus interpolation (105)
Variational image restoration by means of wavelets: simultaneous decomposition (103)
Iteratively Re-weighted Least Squares minimization: Proof of faster than linear rate for sparse recovery (103)
One or Two frequencies? The Synchrosqueezing Answers (100)
Herpesviruses carrying a Brainbow cassette reveal replication and expression of limited numbers of incoming genomes (95)
Regularity of Irregular Subdivision (95)
On the instability of arbitrary biorthogonal wavelet packets (89)
Differential reassignment (88)
Nonlinear Approximation and (Deep) ReLU Networks (88)
Introduction to the special issue on wavelet transforms and multiresolution signal analysis (86)
Normal Multiresolution Approximation of Curves (85)
A New Fully Automated Approach for Aligning and Comparing Shapes (83)
A Bayesian Nonparametric Approach to Image Super-Resolution (80)
One-electron relativistic molecules with Coulomb interaction (78)
Corrigendum/addendum to: Sets of matrices all infinite products of which converge (77)
Quantum‐mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II (76)
Conformal Wasserstein distances: Comparing surfaces in polynomial time (76)
The Canonical Dual Frame of a Wavelet Frame (72)
Crack detection and inpainting for virtual restoration of paintings: The case of the Ghent Altarpiece (70)
Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters (69)
Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate (69)
Detection of forgery in paintings using supervised learning (63)
A/D conversion with imperfect quantizers (62)
Symmetry factored embedding and distance (60)
Capturing Ridge Functions in High Dimensions from Point Queries (60)
On the distributions corresponding to bounded operators in the Weyl quantization (59)
Two theorems on lattice expansions (59)
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity (57)
Quantum Mechanical Path Integrals With Wiener Measures for All Polynomial Hamiltonians (56)
Wavelet-based image decomposition by variational functionals (53)
Othonormal bases of compactly supported wavelets III: better frequency resolution (51)
ON THE THERMODYNAMIC FORMALISM FOR MULTIFRACTAL FUNCTIONS (50)
Nonlinear regularization techniques for seismic tomography (50)
Phase retrieval in infinite-dimensional Hilbert spaces (49)
Symmetry factored embedding and distance (48)
The analysis and design of windowed Fourier frame based multiple description source coding schemes (46)
An integral transform related to quantization (46)
Commutation for Irregular Subdivision (45)
Stable Phase Retrieval in Infinite Dimensions (45)
Erratum: A Simple Wilson Orthonormal Basis with Exponential Decay (43)
Wiener measures for path integrals with affine kinematic variables (42)
Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization (41)
Recent results in wavelet applications (41)
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets (40)
Surface Comparison with Mass Transportation (40)
Robust and Practical Analog-to-Digital Conversion With Exponential Precision (39)
Beta expansions: a new approach to digitally corrected A/D conversion (39)
The pros and cons of democracy (38)
Evaluating Physiological Dynamics via Synchrosqueezing: Prediction of Ventilator Weaning (38)
Stylistic analysis of paintings usingwavelets and machine learning (37)
Analysis of boosting algorithms using the smooth margin function (35)
Physical justiflcation for using the tensor product to describe two quantum systems as one joint system (35)
Continuity statements and counterintuitive examples in connection with Weyl quantization (32)
A study of weyl-heisenberg and wavelet frames (31)
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity (30)
Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms: Application of time-frequency analysis to art investigation (30)
The Golden Ratio Encoder (29)
Conformal Wasserstein distance: II. computational aspects and extensions (29)
Virtual Restoration of the Ghent Altarpiece Using Crack Detection and Inpainting (28)
Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation (27)
Boosting Based on a Smooth Margin (26)
Reconstructing Real-Valued Functions from Unsigned Coefficients with Respect to Wavelet and Other Frames (25)
1. The What, Why, and How of Wavelets (25)
Sparsity-enforcing regularisation and ISTA revisited (24)
Digital Image Processing of The Ghent Altarpiece: Supporting the painting's study and conservation treatment (23)
Multi-Modal Dictionary Learning for Image Separation With Application in Art Investigation (23)
Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion (23)
Different Perspectives on Wavelets (23)
Single-bit oversampled A/D conversion with exponential accuracy in the bit-rate (22)
A Sparse Spectral Method for Homogenization Multiscale Problems (22)
Bayesian crack detection in ultra high resolution multimodal images of paintings (22)
Gaussian Process Landmarking on Manifolds (22)
An integral transform related to quantization. II. Some mathematical properties (22)
One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum (21)
3. Discrete Wavelet Transforms: Frames (21)
Restoration of X-ray fluorescence images of hidden paintings (20)
A characterization of subsystems in physics (19)
Measures for Path Integrals (19)
Removal of Canvas Patterns in Digital Acquisitions of Paintings (19)
Synchrosqueezed Wavelet Transforms: a Tool for Empirical Mode Decomposition (18)
LDMNet: Low Dimensional Manifold Regularized Neural Networks (18)
Coherent states and projective representation of the linear canonical transformations (17)
How does truncation of the mask affect a refinable function? (16)
Bivariate segment approximation and free knot splines: Research problems 96-4 (16)
On Some Iterative Concepts for Image Restoration (16)
Reconstructing Sunyaev-Zeldovich clusters in future CMB experiments (16)
On the Dynamics of Boosting (15)
Optimizing Estimates of Instantaneous Heart Rate from Pulse Wave Signals with the Synchrosqueezing Transform. (15)
Adaptive Gabor transforms (15)
A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation (14)
Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics (14)
Symmetry factored embedding and distance (13)
How Smooth Is the Smoothest Function in a Given Refinable Space (13)
Factoring Wavelet Transforms into Lifting Steps Honours Thesis ( 1997 ) (13)
ariaDNE: A robustly implemented algorithm for Dirichlet energy of the normal (13)
Optimal Stochastic Encoding and Approximation Schemes using Weyl—Heisenberg Sets (13)
An Iteratively Reweighted Least Squares Algorithm for Sparse Regularization (13)
Tree Approximation and Encoding (12)
Constructing measures for path integrals (12)
Recursive Diffeomorphism-Based Regression for Shape Functions (12)
Interpolation of bandlimited functions from quantized irregular samples (12)
Report on Digital Image Processing for Art Historians (12)
Digital cradle removal in X-ray images of art paintings (11)
A decay theorem for refinable functions (11)
Precise Statements of Convergence for AdaBoost and arc-gv (11)
Wavelet transform image coding using trellis coded vector quantization (11)
Spatiogram features to characterize pearls in paintings (10)
Electrocardiographic J Wave and Cardiovascular Outcomes in the General Population (from the Atherosclerosis Risk In Communities Study). (10)
CONFORMAL WASSERSTEIN DISTANCE : II (10)
Artificial intelligence for art investigation: Meeting the challenge of separating x-ray images of the Ghent Altarpiece (10)
Automated J wave detection from digital 12-lead electrocardiogram. (10)
Wavelets: a tool for time-frequency analysis (9)
Different perspectives on wavelets : American Mathematical Society short course, January 11-12, 1993, San Antonio, Texas (9)
Expression of Fractals Through Neural Network Functions (9)
X-ray image separation via coupled dictionary learning (9)
Variational image restoration by means of wavelets (9)
2. The Continuous Wavelet Transform (8)
Identification of Shallow Neural Networks by Fewest Samples (8)
Wavelets and Other Phase Space Localization Methods (8)
Object recognition in art drawings: Transfer of a neural network (7)
A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions (7)
VARIATIONAL BAYESIAN LEARNING FOR WAVELET INDEPENDENT COMPONENT ANALYSIS (7)
8. Symmetry for Compactly Supported Wavelet Bases (7)
Simple proof that the structure preserving maps between quantum mechanical propositional systems conserve the angles (7)
Discrete sets of coherent states and their use in signal analysis (7)
A detailed mathematical study of several aspects of the internet (7)
Harmonic Analysis, Wavelets and Applications (7)
Stable Phase Retrieval from Locally Stable and Conditionally Connected Measurements (6)
9. Characterization of Functional Spaces by Means of Wavelets (6)
Reconstructing dietary ecology of extinct strepsirrhines (Primates, Mammalia) with new approaches for characterizing and analyzing tooth shape (5)
Painting analysis using wavelets and probabilistic topic models (5)
From the original framer to present-day time-frequency and time-scale frames (5)
Optimization of Linear Multiresolution Transforms for Scene Adaptive Coding (4)
ORTHONORMAL BASES OF COHERENT STATES: THE CANONICAL CASE AND THE ax+b-GROUP (4)
A new approach to global seismic tomography based on regularization by sparsity in a novel 3D spherical wavelet basis (4)
Developing Mathematical Tools to Investigate Art (4)
Virtual underpainting reconstruction from X-ray fluorescence imaging data (4)
Wavelets: an overview, with recent applications (4)
Sublinear algorithms for the fourier transform of signals with very few fourier modes: theory, implementations and applications (4)
Data compression and harmonic analysis (invited paper) (4)
Inversion with a sparsity constraint: Application to mantle tomography (3)
Analysis of the truncated Hilbert transform arising in limited data computerized tomography (3)
Measures for more quadratic path integrals (3)
Directional Wavelet Bases Constructions with Dyadic Quincunx Subsampling (3)
A Detailed Study of the Attachment Strategies of New Autonomous Systems in the AS Connectivity Graph (3)
A CONNECTION BETWEEN PROPOSITIONAL SYSTEMS IN HILBERT SPACES AND VON NEUMANN ALGEBRAS (3)
Recent results in wavelet applications (3)
Boosting, margins, and dynamics (3)
A ug 2 00 6 Tomographic inversion using l 1-norm regularization of wavelet coefficients (3)
Variational Bayesian Learning of Sparse Representations and Its Application in Functional Neuroimaging (3)
5. Orthonormal Bases of Wavelets and Multiresolution Analysis (2)
Removing Cradle Artifacts in X-Ray Images of Paintings (2)
Spatiogram features to characterize pearls and beads and other small ball-shaped objects in paintings (2)
On the Matrix Bounds for the Solution Matrix of the Discrete Algebraic Riccati Equation (2)
Adaptive data analysis: theory and applications (2)
Approximating the Riemannian Metric from Point Clouds via Manifold Moving Least Squares (2)
Stop memorizing: A data-dependent regularization framework for intrinsic pattern learning (2)
Conformal Wasserstein Distance: Comparing disk and sphere-type surfaces in polynomial time II, computational aspects (1)
Uncovering elements of style (1)
Remembering Jean Bourgain (1954–2018) (1)
Constructing curvelet-like bases and low-redundancy frames (1)
The cored and logarithm galactic potentials : Periodic orbits and integrability (1)
Opening Address: President of IMU (1)
The work of Yves Meyer (1)
Applied Harmonic Analysis and Sparse Approximation (1)
Stylistic Analysis of Paintings using Complex Wavelets and Random Forest Learning Algorithm (1)
Simpler Alternatives to Information Theoretic Similarity Metrics for Multimodal Image Alignment (1)
Nonlinear Approximation and (Deep) $$\mathrm {ReLU}$$ ReLU Networks (1)
AFFINE COHERENT STATES AND WAVELETS (1)
VII.3 Wavelets and Applications (1)
Wavelets making waves in mathematics and engineering (1)
Big Data Processing in Artwork Analysis (1)
10. Generalizations and Tricks for Orthonormal Wavelet Bases (1)
Open Problem: Does AdaBoost Always Cycle? (1)
Image Separation with Side Information: A Connected Auto-Encoders Based Approach (1)
Neural Network Approximation of Refinable Functions (1)
Independent Component Analysis of spatially distributed patterns of brain activation measured by fMRI (1)
An application of hyperdifferential operators to holomorphic quantization (1)
A Connected Auto-Encoders Based Approach for Image Separation with Side Information: With Applications to Art Investigation (1)
Relativistic Molecules with Coulomb Interaction (1)
Non-Oscillatory Pattern Learning for Non-Stationary Signals (1)
Insights from macroevolutionary modelling and ancestral state reconstruction into the radiation and historical dietary ecology of Lemuriformes (Primates, Mammalia) (1)
Problems in the analysis of complex, high-dimensional datasets (0)
Methods and algorithms for sparsity-based regularization of inverse problems and their application to global seismic tomography (0)
SIMPLERALTERNATIVESTO INFORMATIONTHEORETICSIMILARITYMETRICS FOR MULTIMODAL IMAGEALIGNMENT (0)
L1-norm model constraint for large sparse tomographic system inversion (0)
Tools for Time-Frequency Analysis (0)
The computation of Finite-Frequency kernels without the paraxial approximation. (0)
08492 Abstracts Collection - Structured Decompositions and Efficient Algorithms (0)
Development and assessment of fully automated and globally transitive geometric morphometric methods, with application to a biological comparative dataset with high interspecific variation (0)
Dietary adaptation in lemurs, analyzed using new approaches to describing functional properties of tooth shape (0)
Cradle Removal in X-Ray Images of Panel Paintings (0)
Teaching a computer about shapes in paintings (0)
AN APPLICATION OF HYPERDIFFERENTIAL OPERATORS TO HOLOMORPHIC Q U A N T I Z A T I O N (0)
Image processing for research on the "Ghent altarpiece" (0)
4. Time-Frequency Density and Orthonormal Bases (0)
Steele Prize for Mathematical Exposition (0)
Scale and Space Dependence of Wave Speed Heterogeneity in Global Seismic Models Seen Through the Lense of Wavelet Sparsity (0)
A new Approach to Global Seismic Tomography that Promotes Sparsity with a new Three-Dimensional Wavelet Transform in Spherical Geometry (0)
Regularization on Image Patches: a linear reconstruction from manifold embedding (0)
Submitted to the Annals of Statistics ANALYSIS OF BOOSTING ALGORITHMS USING THE SMOOTH MARGIN FUNCTION ∗ By (0)
Women’s History Month (0)
Mathematics: Muse, Maker, and Measure of the Arts (11w5070) (0)
Pearls and beads in Jan van Eyck’s paintings (0)
MEASURES FOR MORE QUADRATIC PATH INTEGRALS* INGRID DAUBECHIES *~ (0)
Theoretical and experimental analysis of a randomized algorithm for Sparse Fourier transform analysis q (0)
Extracting information from high-dimensional data: probabilistic modeling, inference and evaluation (0)
Squeezed states and path integrals (0)
Non-Convex Planar Harmonic Maps (0)
Insights from macroevolutionary modelling and ancestral state reconstruction into the radiation and historical dietary ecology of Lemuriformes (Primates, Mammalia) (0)
7. More about the Regularity of Compactly Supported Wavelets (0)
Mixed X-Ray Image Separation for Artworks with Concealed Designs (0)
Several algorithms for minimizing variational functionals that favor sparse solutions, with applications (0)
A generalization of the iterative soft-thresholding algorithm for non-separable penalties (0)
Spatiogram features to characterize pearls in the Ghent altarpiece (0)
Tomographic inversion with wavelets and L1-norm penalization (0)
Global tomography using finite-frequency kernels in the wavelet domain (0)
A Learning Based Approach to Separate Mixed X-Ray Images Associated with Artwork with Concealed Designs (0)
Tomographic inversion using L1-regularization of Wavelet Coefficients (0)
Digital Image Processing of The Ghent Altarpiece (0)
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14) (0)
Craquelure inpainting in art work (0)
Automatic segmentation of morphological structure into biologically corresponding features: implications for systematics and ecomorphology (0)
Yves Meyer – Gauss Prize 2010 (0)
08492 Executive Summary - Structured Decompositions and Efficient Algorithms (0)
08492 Abstracts Collection Structured Decompositions and E cient Algorithms Dagstuhl Seminar (0)
Using a family of coherent state representations we obtain in a natural and coordinate independent wayan explicit realization of a projective unitary representation of the symplectic group. Dequantization of these operators gives us the corresponding classical functions. (0)
Wavelet regularization per nullspace shuttle (0)
Applied Harmonic Analysis and Data Processing (0)
Q wavelets Come From ?-A a 1 Point of View (0)
A convergence problem for rational interpolants with preassigned poles: Research problem 96-1 (0)
Building Mathematical Tools to Find Needles in Haystacks (0)
Wiener measures for quantum mechanical path integrals (0)
5.4 Precomputation for Inverse Problems Figure 10: Patches of Gridpoints at Various Radii from 0 5.3 Eecient Storage of Complicated Maps 5.2 Fast Approximate Jacobians (0)
The New IMU Needs You (0)
Comparison of novel regularization techniques in seismic tomography (0)

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