# Gitta Kutyniok

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German applied mathematician

## Gitta Kutyniok's AcademicInfluence.com Rankings

Gitta Kutyniokmathematics Degrees

Mathematics

#4529

World Rank

#6417

Historical Rank

Harmonic Analysis

#13

World Rank

#14

Historical Rank

Applied Mathematics

#265

World Rank

#290

Historical Rank

Measure Theory

#1634

World Rank

#2015

Historical Rank

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Mathematics

## Gitta Kutyniok's Degrees

- PhD Mathematics University of Potsdam

## Why Is Gitta Kutyniok Influential?

(Suggest an Edit or Addition)According to Wikipedia, Gitta Kutyniok is a German applied mathematician known for her research in harmonic analysis, deep learning, compressed sensing, and image processing. She has a Bavarian AI Chair for "Mathematical Foundations of Artificial Intelligence" in the institute of mathematics at the Ludwig Maximilian University of Munich.

## Gitta Kutyniok's Published Works

### Published Works

- Compressed Sensing: Theory and Applications (2012) (928)
- Sparse multidimensional representation using shearlets (2005) (539)
- Frames of subspaces (2003) (403)
- Fusion frames and distributed processing (2006) (351)
- Shearlets: Multiscale Analysis for Multivariate Data (2012) (308)
- Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators (2006) (306)
- Compactly supported shearlets are optimally sparse (2010) (294)
- Resolution of the wavefront set using continuous shearlets (2006) (290)
- Introduction to compressed sensing (2012) (249)
- Finite Frames: Theory and Applications (2012) (241)
- Optimal Approximation with Sparsely Connected Deep Neural Networks (2017) (217)
- Construction of Compactly Supported Shearlet Frames (2010) (214)
- FRAMES OF SUBSPACES. WAVELETS, FRAMES AND OPERATOR THEORY (2004) (181)
- Shearlet coorbit spaces and associated Banach frames (2009) (178)
- A Haar wavelet-based perceptual similarity index for image quality assessment (2016) (177)
- The Uncertainty Principle Associated with the Continuous Shearlet Transform (2008) (152)
- A Theoretical Analysis of Deep Neural Networks and Parametric PDEs (2019) (143)
- Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms (2019) (125)
- ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm (2011) (120)
- ShearLab 3D (2014) (116)
- Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography (2018) (110)
- Microlocal Analysis of the Geometric Separation Problem (2010) (110)
- Robust dimension reduction, fusion frames, and Grassmannian packings (2007) (108)
- Compactly Supported Shearlets (2010) (108)
- Introduction to Shearlets (2012) (105)
- Sparse Recovery From Combined Fusion Frame Measurements (2009) (104)
- Theory and applications of compressed sensing (2012) (95)
- Compressed Sensing: List of contributors (2012) (89)
- Approximation Spaces of Deep Neural Networks (2019) (85)
- Image Separation Using Wavelets and Shearlets (2010) (82)
- Irregular Shearlet Frames: Geometry and Approximation Properties (2010) (78)
- Introduction to Finite Frame Theory (2013) (77)
- Parabolic Molecules (2012) (76)
- Transferability of Spectral Graph Convolutional Neural Networks (2019) (75)
- Duality Principles in Frame Theory (2004) (74)
- Robustness of Fusion Frames under Erasures of Subspaces and of Local Frame Vectors (2007) (67)
- ShearLab 3D: Faithful Digital Shearlet Transforms Based on Compactly Supported Shearlets (2016) (67)
- Shearlets on Bounded Domains (2010) (66)
- Image Separation Using Shearlets (2011) (63)
- Modeling sensor networks with fusion frames (2007) (62)
- Data Separation by Sparse Representations (2011) (61)
- Scalable Frames (2012) (61)
- The Balian–Low theorem for symplectic lattices in higher dimensions (2002) (61)
- Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis (2007) (56)
- Optimally Sparse Frames (2010) (56)
- Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames (2011) (55)
- Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks (2020) (55)
- Sparse fusion frames: existence and construction (2011) (54)
- The Modern Mathematics of Deep Learning (2021) (54)
- CONSTRUCTION OF REGULAR AND IRREGULAR SHEARLET FRAMES (2007) (53)
- Density of weighted wavelet frames (2003) (52)
- A new identity for Parseval frames (2007) (51)
- Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis (2012) (51)
- Classification of Edges Using Compactly Supported Shearlets (2014) (50)
- Digital Shearlet Transforms (2011) (49)
- Wilson Bases for General Time-Frequency Lattices (2003) (49)
- $\ell^1$-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed? (2017) (48)
- Zeros of the Zak transform on locally compact abelian groups (1998) (48)
- RadioUNet: Fast Radio Map Estimation With Convolutional Neural Networks (2019) (47)
- A generalization of Gram–Schmidt orthogonalization generating all Parseval frames (2007) (43)
- On the Transferability of Spectral Graph Filters (2019) (43)
- A quantitative notion of redundancy for finite frames (2009) (41)
- Adaptive Multiresolution Analysis Structures and Shearlet Systems (2011) (41)
- Asymptotic Analysis of Inpainting via Universal Shearlet Systems (2014) (38)
- The geometry of sets of parameters of wave packet frames (2006) (37)
- Development of a digital shearlet transform based on Pseudo-Polar FFT (2009) (36)
- Optimal Compressive Imaging of Fourier Data (2015) (34)
- The theory of reproducing systems on locally compact abelian groups (2006) (34)
- The Computational Complexity of Understanding Binary Classifier Decisions (2021) (33)
- Geometric Separation using a Wavelet-Shearlet Dictionary (2010) (33)
- Expressivity of Deep Neural Networks (2020) (33)
- Compressed Sensing for Finite-Valued Signals (2016) (33)
- A Rate-Distortion Framework for Explaining Neural Network Decisions (2019) (30)
- Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements (2014) (29)
- Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data (2015) (28)
- ChatGPT for good? On opportunities and challenges of large language models for education (2023) (27)
- PROMP: A sparse recovery approach to lattice-valued signals (2017) (27)
- Sparsity and spectral properties of dual frames (2012) (26)
- Landau's necessary density conditions for LCA groups (2008) (26)
- From Wavelets to Shearlets and back again (2007) (26)
- Affine Density in Wavelet Analysis (2007) (26)
- Gabor Shearlets (2013) (24)
- Linear independence of time-frequency shifts under a generalized Schrödinger representation (2002) (24)
- Scalable Frames and Convex Geometry (2013) (23)
- Shearlets and Optimally Sparse Approximations (2011) (23)
- Decompositions of frames and a new frame identity (2005) (23)
- Measures of Scalability (2014) (23)
- The Homogeneous Approximation Property for wavelet frames (2007) (23)
- Analysis of data separation and recovery problems using clustered sparsity (2011) (23)
- A redundant version of the Rado–Horn Theorem (2006) (22)
- A decomposition theorem for frames and the Feichtinger Conjecture (2007) (22)
- Cartoon Approximation with -Curvelets (2014) (21)
- Beurling Dimension of Gabor Pseudoframes for Affine Subspaces (2008) (21)
- Geometric Separation by Single-Pass Alternating Thresholding (2012) (21)
- Image interpolation using shearlet based iterative refinement (2013) (20)
- Ambiguity functions, Wigner distributions and Cohen's class for LCA groups (2003) (20)
- Alpha molecules: curvelets, shearlets, ridgelets, and beyond (2013) (19)
- Image inpainting: theoretical analysis and comparison of algorithms (2013) (19)
- Density of frames and Schauder bases of windowed exponentials (2008) (18)
- Fusion frames and robust dimension reduction (2008) (17)
- Clustered Sparsity and Separation of Cartoon and Texture (2012) (17)
- Transferability of Graph Neural Networks: an Extended Graphon Approach (2021) (16)
- Shearlets: Theory and Applications (2014) (16)
- Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm (2019) (15)
- Affine Density, Frame Bounds, and the Admissibility Condition for Wavelet Frames (2007) (15)
- OPERATORS AND FRAMES (2012) (15)
- Tensor network approaches for learning non-linear dynamical laws (2020) (15)
- Compressed Sensing for Analog Signals (2018) (14)
- A Survey of Compressed Sensing (2015) (14)
- A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations (2016) (14)
- A RATIONAL DESIGN OF A DIGITAL SHEARLET TRANSFORM (2010) (14)
- Compressed sensing for fusion frames (2009) (13)
- Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory? (2020) (13)
- Pathloss Prediction using Deep Learning with Applications to Cellular Optimization and Efficient D2D Link Scheduling (2020) (13)
- A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups (2003) (13)
- Compressed Sensing and its Applications: MATHEON Workshop 2013 (2015) (13)
- Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting (2017) (13)
- Cartoon Approximation with $$\alpha $$α-Curvelets (2014) (13)
- Sparsity Equivalence of Anisotropic Decompositions (2011) (12)
- Unification of sparse Bayesian learning algorithms for electromagnetic brain imaging with the majorization minimization framework (2020) (12)
- Regularization and numerical solution of the inverse scattering problem using shearlet frames (2014) (12)
- Hierarchical Sparse Channel Estimation for Massive MIMO (2018) (11)
- Generalization Analysis of Message Passing Neural Networks on Large Random Graphs (2022) (11)
- Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks (2019) (11)
- Efficient Resolution of Anisotropic Structures (2014) (11)
- The local integrability condition for wavelet frames (2006) (11)
- OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs (2022) (10)
- Limitations of Deep Learning for Inverse Problems on Digital Hardware (2022) (10)
- A Unitary Extension Principle for Shearlet Systems (2009) (10)
- Practical Implementation of Compressive Sensing for High Resolution STEM (2016) (10)
- BEURLING DENSITY AND SHIFT-INVARIANT WEIGHTED IRREGULAR GABOR SYSTEMS (2005) (10)
- Interval Neural Networks: Uncertainty Scores (2020) (10)
- BEURLING DENSITY AND SHIFT-INVARIANT WEIGHTED IRREGULAR GABOR SYSTEMS (2005) (10)
- A weak qualitative uncertainty principle for compact groups (2003) (10)
- Duality principles, localization of frames, and Gabor theory (2005) (9)
- Erasure-proof transmissions: fusion frames meet coding theory (2009) (9)
- Adaptive anisotropic Petrov-Galerkin methods for first order transport equations (2016) (9)
- The Effect of Perturbations of Frame Sequences and Fusion Frames on Their Duals (2015) (9)
- FUSION FRAMES: EXISTENCE AND CONSTRUCTION (2009) (9)
- Dualizable Shearlet Frames and Sparse Approximation (2014) (8)
- α-Molecules : Curvelets , Shearlets , Ridgelets , and Beyond (2013) (8)
- Image interpolation using shearlet based sparsity priors (2013) (8)
- Computation of the density of weighted wavelet systems (2003) (8)
- A Rate-Distortion Framework for Explaining Black-box Model Decisions (2021) (7)
- Explaining Neural Network Decisions Is Hard (2020) (6)
- Anisotropic multiscale systems on bounded domains (2015) (6)
- Constructing fusion frames with desired parameters (2009) (6)
- tfShearlab: The TensorFlow Digital Shearlet Transform for Deep Learning (2020) (6)
- Memory-optimal neural network approximation (2017) (6)
- The Mismatch Principle: The Generalized Lasso Under Large Model Uncertainties. (2019) (5)
- Detecting failure modes in image reconstructions with interval neural network uncertainty (2021) (5)
- In-Distribution Interpretability for Challenging Modalities (2020) (5)
- Parabolic Molecules: Curvelets, Shearlets, and Beyond (2014) (5)
- OPTIMALLY SPARSE FUSION FRAMES : EXISTENCE AND CONSTRUCTION (2010) (5)
- Perfect Preconditioning of Frames by a Diagonal Operator (2013) (4)
- Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization (2022) (4)
- The Computational Complexity of Understanding Network Decisions (2019) (4)
- Dataset of Pathloss and ToA Radio Maps With Localization Application (2022) (4)
- A Theoretical Analysis of Deep Neural Networks and Parametric PDEs (2021) (4)
- Cartoon Explanations of Image Classifiers (2021) (4)
- The Effect of Perturbations of Operator-Valued Frame Sequences and Fusion Frames on Their Duals (2015) (4)
- Stability and Generalization Capabilities of Message Passing Graph Neural Networks (2022) (4)
- A fundamental identity for Parseval frames (2005) (4)
- Real-time Outdoor Localization Using Radio Maps: A Deep Learning Approach (2021) (3)
- Estimation of Angles of Arrival Through Superresolution -- A Soft Recovery Approach for General Antenna Geometries (2017) (3)
- Deep Microlocal Reconstruction for Limited-Angle Tomography (2021) (3)
- LocUNet: Fast Urban Positioning Using Radio Maps and Deep Learning (2022) (3)
- Signal recovery from thresholded frame measurements (2013) (3)
- Analysis of simultaneous inpainting and geometric separation based on sparse decomposition (2020) (3)
- Analysis of lscr1 minimization in the Geometric Separation Problem (2008) (3)
- Inverse Problems Are Solvable on Real Number Signal Processing Hardware (2022) (3)
- The Restricted Isometry of ReLU Networks: Generalization through Norm Concentration (2020) (3)
- Average case analysis of sparse recovery from combined fusion frame measurements (2010) (2)
- Upper and lower redundancy of finite frames (2010) (2)
- Shearlet Analysis of Confocal Laser-Scanning Microscopy Images to Extract Morphological Features of Neurons (2014) (2)
- Geometric Multiscale Analysis : From Wavelets to Parabolic Molecules (2014) (2)
- A low complexity replacement scheme for erased frame coefficients (2009) (2)
- (Non-)existence of Wilson bases for general time-frequency lattices (2003) (2)
- CONVOLUTION AND WIENER AMALGAM SPACES ON THE AFFINE GROUP (2008) (2)
- Compressed Sensing: Preface (2012) (2)
- Preconditioning of frames (2013) (2)
- Error Correction for Erasures of Quantized Frame Coefficients (2010) (2)
- Coarse quantization with the fast digital shearlet transform (2011) (2)
- Sparse matrices in frame theory (2014) (2)
- Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function” (2020) (2)
- The Mismatch Principle: Statistical Learning Under Large Model Uncertainties (2018) (2)
- A DECOMPOSITION THEOREM FOR FRAMES AND THE WEAK FEICHTINGER CONJECTURE (2005) (2)
- A Compressed Sensing Approach to Component Separation in Imaging (2014) (1)
- Construction of Compactly Supported Shearlet Frames (2011) (1)
- What is Applied Harmonic Analysis? (2008) (1)
- Well-definedness of Physical Law Learning: The Uniqueness Problem (2022) (1)
- Special Issue on the Mathematical Foundations of Deep Learning in Imaging Science (2020) (1)
- Graph Scattering beyond Wavelet Shackles (2023) (1)
- Erasure-proof coding with fusion frames (2009) (1)
- Real-time Localization Using Radio Maps (2020) (1)
- Digital Shearlet Transform (2011) (1)
- Guest Editorial: Mathematics and Image Analysis (2015) (1)
- Complexity bounds for approximations with deep ReLU neural networks in Sobolev norms (2019) (1)
- Reconstruction of finite-valued sparse signals (2017) (1)
- Accumulative density (2005) (1)
- Preface to the Special Issue on Sparse Approximate Solution of Linear Systems (2014) (1)
- Mini-Workshop: Shearlets (2010) (1)
- Applied Harmonic Analysis and Sparse Approximation (2012) (1)
- Quasi Monte Carlo Time-Frequency Analysis (2020) (1)
- Operators and frames - Corrigendum (2017) (1)
- New Discretization Methods for the Numerical Approximation of PDEs (2015) (1)
- OPTIMAL APPROXIMATION WITH SPARSELY CONNECTED DEEP NEURAL (2019) (1)
- Learning sparse representations on the sphere (2018) (0)
- OPTIMALLY SPARSE APPROXIMATIONS OF MULTIVARIATE FUNCTIONS USING COMPACTLY SUPPORTED SHEARLET FRAMES (2011) (0)
- Wavelets in Neurophysiology (0)
- Operator algebras and representation theory : frames, wavelets and fractals (2011) (0)
- A QUANTITATIVE NOTION OF REDUNDANCY AND ITS APPLICATIONS (2011) (0)
- A Compressed Sensing Approach to Select Optimal Atom-Centered Basis Functions for DFT and Beyond (2016) (0)
- Memorization-Dilation: Modeling Neural Collapse Under Noise (2022) (0)
- Ju l 2 01 4 α-Molecules (2014) (0)
- JMIV Special Issue Mathematics and Image Analysis (2017) (0)
- Fusion Frames and Wireless Sensor Networks (2013) (0)
- Compressed sensing in Hilbert spaces (2018) (0)
- Anisotropic multiscale systems on bounded domains (2020) (0)
- 110 11051 – Sparse Representations and Efficient Sensing of Data 2 Table of Contents Executive Summary (2011) (0)
- Compressed Sensing (2014) (0)
- FRAMES AND THE KADISON-SINGER PROBLEM : A REPORT FOR AIM (2008) (0)
- Brigitte Forster, Peter Massopust (eds.): “Four Short Courses on Harmonic Analysis” (2011) (0)
- Complexity Blowup for Solutions of the Laplace and the Diffusion Equation (2022) (0)
- Sparse Representations and Efficient Sensing of Data (Dagstuhl Seminar 11051) (2011) (0)
- 08492 Abstracts Collection - Structured Decompositions and Efficient Algorithms (2008) (0)
- Compressed Sensing: From Theory to Praxis (2017) (0)
- Efficient Approximation of Solutions of Parametric PDEs by ReLU Neural Networks (2019) (0)
- Non-Computability of the Pseudoinverse on Digital Computers (2022) (0)
- 1 Data Separation by Sparse Representations (2011) (0)
- ROB volume 30 issue 5 Cover and Back matter (2012) (0)
- Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data (2017) (0)
- A Human-Goal-Based Approach to the Analysis and Processing of Visibility Data (2010) (0)
- Preface (2012) (0)
- 1 . 2 Sparsity : A Reasonable Assumption ? (2012) (0)
- A generalization of the iterative soft-thresholding algorithm for non-separable penalties (2012) (0)
- Spectral properties of dual frames (2013) (0)
- Computability of Optimizers (2023) (0)
- Innovative Approaches to the Numerical Approximation of PDEs (2020) (0)
- Preface to the Special Issue of ILAS 2019: Linear Algebra without Borders, The 22nd ILAS Conference, Rio de Janeiro, Brazil, July 08–12, 2019 (2020) (0)
- Shearlets: From Theory to Deep Learning (2021) (0)
- Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis (2013) (0)
- Applied Harmonic Analysis and Data Science (2022) (0)
- The Oracle of DLphi (2019) (0)
- A New Perspective on `-Analysis Recovery (2019) (0)
- Chapter 1 A Survey of Compressed Sensing (2014) (0)
- Deep Recurrent Brain Source Imaging (2019) (0)
- Mathematics in Telecommunications (2019) (0)
- JMIV Special Issue Mathematics and Image Analysis (2011) (0)
- Applied Harmonic Analysis and Data Processing (2019) (0)
- Perturbations of fusion frames and the effect on their canonical dual (2015) (0)
- Compressed Sensing: Frontmatter (2012) (0)
- Memorization-Dilation: Modeling Neural Collapse Under Label Noise (2022) (0)
- Sparse matrices in frame theory (2013) (0)
- Dualizable Shearlet Frames and Sparse Approximation (2016) (0)
- N A ] 2 3 Fe b 20 14 A ShearLab 3 D : Faithful Digital Shearlet Transforms based on Compactly Supported (2014) (0)
- THE LOCAL INTEGRABILITY CONDITION FOR WAVELET (2005) (0)
- Artificial Neural Networks by Martin Genzel and (2019) (0)
- Guest Editorial: Mathematics and Image Analysis (2015) (0)
- Chapter 1 Introduction to Finite Frame Theory (2019) (0)
- Preface of the guest‐editors (2014) (0)
- Name and Surname University City/State Country Position (2015) (0)
- The Uniqueness Problem of Physical Law Learning (2023) (0)
- A Rate-Distortion Framework for Explaining Deep Neural Network Decisions (2019) (0)
- Sparse Representations, Numerical Linear Algebra, and Optimization (2014) (0)
- Unveiling the Sampling Density in Non-Uniform Geometric Graphs (2022) (0)
- 08492 Abstracts Collection Structured Decompositions and E cient Algorithms Dagstuhl Seminar (2009) (0)
- Special Issue on the Mathematical Foundations of Deep Learning in Imaging Science (2020) (0)
- FRAMES AND THE KADISON-SINGER PROBLEM (0)
- Parabolic Molecules (2013) (0)
- Sparse and Low Rank Approximation ( 11 w 5036 ) (2011) (0)
- Approximation Spaces of Deep Neural Networks (2021) (0)
- 2 Measure for Sparse Approximation and Optimality (2018) (0)
- Chapter 1 Fusion Frames (2012) (0)
- Explaining Image Classifiers with Multiscale Directional Image Representation (2022) (0)
- Frame theory intersects geometry organized by (2019) (0)
- Frames from first principles : Error correction , symmetry goals , and numerical efficiency (2009) (0)
- 08492 Executive Summary - Structured Decompositions and Efficient Algorithms (2008) (0)
- Applied Harmonic Analysis meets Sparse Regularization of Operator Equations (2016) (0)
- The Mathematics of Artificial Intelligence (2022) (0)
- Stochastic Signal Processing in Phase Space (2019) (0)

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## What Schools Are Affiliated With Gitta Kutyniok?

Gitta Kutyniok is affiliated with the following schools: