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Author ID: kutyniok.gitta Recent zbMATH articles by "Kutyniok, Gitta"
Published as: Kutyniok, Gitta
Homepage: https://www.ai.math.uni-muenchen.de/members/professor/kutyniok/index.html
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Videos: carmin.tv
all top 5

Co-Authors

19 single-authored
17 Casazza, Peter George
16 Lim, Wang-Q
12 Petersen, Philipp Christian
10 Boche, Holger
9 Grohs, Philipp
8 Rauhut, Holger
6 Calderbank, Arthur Robert
6 Labate, Demetrio
5 Daubechies, Ingrid
5 Heil, Christopher E.
5 Lemvig, Jakob
5 Philipp, Friedrich
5 Strohmer, Thomas
5 Zhuang, Xiaosheng
4 Andrade-Loarca, Hector
4 Dahlke, Stephan
4 Keiper, Sandra
4 Levie, Ron
4 Raslan, Mones
4 Speegle, Darrin M.
3 Bacho, Aras
3 Fono, Adalbert
3 Krahmer, Felix
3 März, Maximilian
3 Okoudjou, Kasso A.
3 Öktem, Ozan
3 Schafer, Martin
3 Steidl, Gabriele
2 Berner, Julius
2 Bodmann, Bernhard G.
2 Cahill, Jameson
2 Caire, Giuseppe
2 Czaja, Wojciech
2 Dahmen, Wolfgang A.
2 Flinth, Axel
2 Genzel, Martin
2 Gröchenig, Karlheinz
2 Gühring, Ingo
2 Han, Bin
2 Heinecke, Andreas
2 Jørgensen, Palle E. T.
2 Kittipoom, Pisamai
2 Ma, Jackie
2 Mathar, Rudolf
2 Ólafsson, Gestur
2 Pezeshki, Ali
2 Sauer, Tomas
2 Schneider, Reinhold
2 Scholl, Philipp
2 Schwab, Christoph
2 Shen, Zuowei
2 Silvestrov, Sergei D.
2 Stevenson, Rob P.
2 Teschke, Gerd
2 Vybíral, Jan
2 Welper, Gerrit
1 Adcock, Ben
1 Avron, Haim
1 Balan, Radu V.
1 Bieker, Katharina
1 Bodmann, Bernard G.
1 Bölcskei, Helmut
1 Boufounos, Petros T.
1 Bronstein, Michael M.
1 Bruna, Joan
1 Bubba, Tatiana A.
1 Bucci, Lorenzo
1 Chen, Xuemei
1 Cremers, Daniel
1 de Abreu, Nair Maria Maia
1 Do, Van Tiep
1 Donoho, David Leigh
1 Edidin, Dan
1 Eisert, Jens
1 Geist, Moritz
1 Goeßmann, Alex
1 Götte, Michael
1 Gribonval, Rémi
1 Guo, Kanghui
1 Haber, Eldad
1 Haddadin, Sami
1 Han, Deguang
1 Hansen, Anders C.
1 Hauch, Sascha
1 Hege, Julius
1 Helmberg, Christoph
1 Huang, Chunyan
1 Huang, Wei
1 Jung, Jaesug
1 Kaniuth, Eberhard
1 King, Emily Jeannette
1 Kornelson, Keri A.
1 Kunsch, Robert J.
1 Kussaba, Hugo Tadashi M.
1 Lammers, Mark C.
1 Larson, David Royal
1 Lassas, Matti J.
1 Lee, Dae Gwan
1 Lee, Yunseok
1 Li, Shidong
...and 36 more Co-Authors
all top 5

Serials

15 Applied and Computational Harmonic Analysis
9 Oberwolfach Reports
6 Linear Algebra and its Applications
6 Applied and Numerical Harmonic Analysis
5 IEEE Transactions on Information Theory
5 Constructive Approximation
5 SIAM Journal on Imaging Sciences
4 SIAM Journal on Mathematical Analysis
4 The Journal of Fourier Analysis and Applications
3 Journal of Mathematical Analysis and Applications
3 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
3 Proceedings of the American Mathematical Society
3 Advances in Computational Mathematics
3 GAMM-Mitteilungen
2 Journal of Approximation Theory
2 Journal of Operator Theory
2 The Journal of Geometric Analysis
2 Journal of Mathematical Imaging and Vision
2 Analysis and Applications (Singapore)
1 Communications on Pure and Applied Mathematics
1 Houston Journal of Mathematics
1 Inverse Problems
1 ACM Transactions on Mathematical Software
1 Archiv der Mathematik
1 Colloquium Mathematicum
1 Illinois Journal of Mathematics
1 Journal of Computational and Applied Mathematics
1 Journal of Functional Analysis
1 Numerical Functional Analysis and Optimization
1 SIAM Journal on Numerical Analysis
1 Transactions of the American Mathematical Society
1 Internationale Mathematische Nachrichten
1 Journal of Scientific Computing
1 Computational Statistics
1 Journal of Inverse and Ill-Posed Problems
1 The Journal of Artificial Intelligence Research (JAIR)
1 Foundations of Computational Mathematics
1 Journal of Machine Learning Research (JMLR)
1 Sampling Theory in Signal and Image Processing
1 International Journal of Wavelets, Multiresolution and Information Processing
1 The Journal of Mathematical Sciences. New Series
1 Lecture Notes in Mathematics
1 Operators and Matrices
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 SIAM Journal on Mathematics of Data Science

Publications by Year

Citations contained in zbMATH Open

110 Publications have been cited 2,734 times in 1,443 Documents Cited by Year
Frames of subspaces. Zbl 1058.42019
Casazza, Peter G.; Kutyniok, Gitta
239
2004
Fusion frames and distributed processing. Zbl 1258.42029
Casazza, Peter G.; Kutyniok, Gitta; Li, Shidong
184
2008
Finite frames. Theory and applications. Zbl 1257.42001
165
2013
Resolution of the wavefront set using continuous shearlets. Zbl 1169.42012
Kutyniok, Gitta; Labate, Demetrio
110
2009
Sparse multidimensional representations using anisotropic dilation and shear operators. Zbl 1099.65148
Guo, Kanghui; Kutyniok, Gitta; Labate, Demetrio
97
2006
Optimal approximation with sparsely connected deep neural networks. Zbl 1499.41029
Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
97
2019
Shearlets. Multiscale analysis for multivariate data. Zbl 1237.42001
95
2012
Shearlet coorbit spaces and associated Banach frames. Zbl 1171.42019
Dahlke, Stephan; Kutyniok, Gitta; Steidl, Gabriele; Teschke, Gerd
87
2009
The uncertainty principle associated with the continuous shearlet transform. Zbl 1257.42047
Dahlke, Stephan; Kutyniok, Gitta; Maass, Peter; Sagiv, Chen; Stark, Hans-Georg; Teschke, Gerd
79
2008
Compactly supported shearlets are optimally sparse. Zbl 1226.42031
Kutyniok, Gitta; Lim, Wang-Q
63
2011
Error bounds for approximations with deep ReLU neural networks in \(W^{s , p}\) norms. Zbl 1452.41009
Gühring, Ingo; Kutyniok, Gitta; Petersen, Philipp
61
2020
A theoretical analysis of deep neural networks and parametric PDEs. Zbl 07493717
Kutyniok, Gitta; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold
59
2022
Construction of compactly supported shearlet frames. Zbl 1239.42031
Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q
49
2012
Robust dimension reduction, fusion frames, and Grassmannian packings. Zbl 1283.42046
Kutyniok, Gitta; Pezeshki, Ali; Calderbank, Robert; Liu, Taotao
44
2009
Scalable frames. Zbl 1260.42023
Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Tuley, Elizabeth K.
41
2013
Introduction to shearlets. Zbl 1251.42010
Kutyniok, Gitta; Labate, Demetrio
41
2012
Duality principles in frame theory. Zbl 1058.42020
Casazza, Peter G.; Kutyniok, Gitta; Lammers, Mark C.
40
2004
Microlocal analysis of the geometric separation problem. Zbl 1261.94007
Donoho, David; Kutyniok, Gitta
38
2013
Zeros of the Zak transform on locally compact Abelian groups. Zbl 0907.43005
Kaniuth, Eberhard; Kutyniok, Gitta
36
1998
A new identity for Parseval frames. Zbl 1136.42308
Balan, Radu; Casazza, Peter G.; Edidin, Dan; Kutyniok, Gitta
35
2007
Parabolic molecules. Zbl 1403.42038
Grohs, Philipp; Kutyniok, Gitta
34
2014
Approximation spaces of deep neural networks. Zbl 1491.82017
Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix
33
2022
Robustness of fusion frames under erasures of subspaces and of local frame vectors. Zbl 1256.94017
Casazza, Peter G.; Kutyniok, Gitta
33
2008
Optimally sparse approximations of 3D functions by compactly supported shearlet frames. Zbl 1252.42043
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
28
2012
Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography. Zbl 1416.92099
Bubba, Tatiana A.; Kutyniok, Gitta; Lassas, Matti; März, Maximilian; Samek, Wojciech; Siltanen, Samuli; Srinivasan, Vignesh
28
2019
Numerical solution of the parametric diffusion equation by deep neural networks. Zbl 1473.35331
Geist, Moritz; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold; Kutyniok, Gitta
26
2021
Sparse fusion frames: existence and construction. Zbl 1264.94042
Calderbank, Robert; Casazza, Peter G.; Heinecke, Andreas; Kutyniok, Gitta; Pezeshki, Ali
26
2011
ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. Zbl 1347.65203
Kutyniok, Gitta; Lim, Wang-Q; Reisenhofer, Rafael
26
2016
Density of weighted wavelet frames. Zbl 1029.42031
Heil, Christopher; Kutyniok, Gitta
25
2003
Introduction to finite frame theory. Zbl 1281.42032
Casazza, Peter G.; Kutyniok, Gitta; Philipp, Friedrich
24
2013
Analysis of inpainting via clustered sparsity and microlocal analysis. Zbl 1362.94007
King, Emily J.; Kutyniok, Gitta; Zhuang, Xiaosheng
24
2014
The geometry of sets of parameters of wave packet frames. Zbl 1095.42020
Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin
23
2006
Classification of edges using compactly supported shearlets. Zbl 1378.42023
Kutyniok, Gitta; Petersen, Philipp
23
2017
The Balian-Low theorem for symplectic lattices in higher dimensions. Zbl 1017.42027
Gröchenig, Karlheinz; Han, Deguang; Heil, Christopher; Kutyniok, Gitta
22
2002
Optimally sparse frames. Zbl 1365.94059
Casazza, Peter G.; Heinecke, Andreas; Krahmer, Felix; Kutyniok, Gitta
22
2011
The theory of reproducing systems on locally compact abelian groups. Zbl 1113.43008
Kutyniok, Gitta; Labate, Demetrio
22
2006
ShearLab: a rational design of a digital parabolic scaling algorithm. Zbl 1257.42048
Kutyniok, Gitta; Shahram, Morteza; Zhuang, Xiaosheng
22
2012
Sparse recovery from combined fusion frame measurements. Zbl 1365.94066
Boufounos, Petros; Kutyniok, Gitta; Rauhut, Holger
20
2011
Affine density in wavelet analysis. Zbl 1142.42017
Kutyniok, Gitta
19
2007
Adaptive directional subdivision schemes and shearlet multiresolution analysis. Zbl 1193.42127
Kutyniok, Gitta; Sauer, Tomas
19
2009
Beurling dimension of Gabor pseudoframes for affine subspaces. Zbl 1268.42055
Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin
17
2008
Adaptive multiresolution analysis structures and shearlet systems. Zbl 1283.42053
Han, Bin; Kutyniok, Gitta; Shen, Zuowei
17
2011
Linear stable sampling rate: optimality of 2D wavelet reconstructions from Fourier measurements. Zbl 1331.42036
Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie
16
2015
The homogeneous approximation property for wavelet frames. Zbl 1133.42049
Heil, Christopher; Kutyniok, Gitta
16
2007
Landau’s necessary density conditions for LCA groups. Zbl 1158.43004
Gröchenig, Karlheinz; Kutyniok, Gitta; Seip, Kristian
16
2008
\(\alpha\)-Molecules. Zbl 1342.42041
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
15
2016
A quantitative notion of redundancy for finite frames. Zbl 1211.42027
Bodmann, Bernhard G.; Casazza, Peter G.; Kutyniok, Gitta
15
2011
Theory and applications of compressed sensing. Zbl 1283.94018
Kutyniok, Gitta
15
2013
A survey of compressed sensing. Zbl 1333.94015
Boche, Holger; Calderbank, Robert; Kutyniok, Gitta; Vybíral, Jan
13
2015
Compactly supported shearlets. Zbl 1252.42042
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
13
2012
Image separation using wavelets and shearlets. Zbl 1345.94007
Kutyniok, Gitta; Lim, Wang-Q
13
2012
Asymptotic analysis of inpainting via universal shearlet systems. Zbl 1307.42033
Genzel, Martin; Kutyniok, Gitta
13
2014
The modern mathematics of deep learning. (Die moderne Mathematik des tiefen Lernens.) Zbl 07571594
Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
13
2021
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames. Zbl 1118.65027
Casazza, Peter G.; Kutyniok, Gitta
12
2007
Fusion frames. Zbl 1261.42048
Casazza, Peter G.; Kutyniok, Gitta
12
2013
Wilson bases for general time-frequency lattices. Zbl 1090.94008
Kutyniok, Gitta; Strohmer, Thomas
12
2005
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. Zbl 1439.35009
Andrade-Loarca, Hector; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp C.
11
2019
\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed? Zbl 1460.94021
Genzel, Martin; Kutyniok, Gitta; März, Maximilian
11
2021
Sparsity and spectral properties of dual frames. Zbl 1280.42026
Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob
11
2013
Optimal compressive imaging of Fourier data. Zbl 1437.94043
Kutyniok, Gitta; Lim, Wang-Q
11
2018
Measures of scalability. Zbl 1359.94307
Chen, Xuemei; Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Wang, Rongrong
10
2015
Geometric separation by single-pass alternating thresholding. Zbl 1357.42033
Kutyniok, Gitta
10
2014
Cartoon approximation with \(\alpha\)-curvelets. Zbl 1359.42018
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
10
2016
Gabor shearlets. Zbl 1304.42084
Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng
10
2015
Scalable frames and convex geometry. Zbl 1307.42029
Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich
10
2014
A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups. Zbl 1023.43003
Kutyniok, Gitta
9
2003
Linear independence of time-frequency shifts under a generalized Schrödinger representation. Zbl 0997.43006
Kutyniok, Gitta
9
2002
Affine density, frame bounds, and the admissibility condition for wavelet frames. Zbl 1124.42027
Kutyniok, Gitta
9
2007
The computational complexity of understanding binary classifier decisions. Zbl 1512.68116
Wäldchen, Stephan; Macdonald, Jan; Hauch, Sascha; Kutyniok, Gitta
9
2021
Digital shearlet transforms. Zbl 1255.94021
Kutyniok, Gitta; Lim, Wang-Q; Zhuang, Xiaosheng
9
2012
Ambiguity functions, Wigner distributions and Cohen’s class for LCA groups. Zbl 1032.43002
Kutyniok, Gitta
8
2003
Time-frequency analysis on locally compact groups. Zbl 0971.43001
Kutyniok, Gitta
8
2000
PROMP: a sparse recovery approach to lattice-valued signals. Zbl 1408.94862
Flinth, Axel; Kutyniok, Gitta
8
2018
Operators and frames. Zbl 1289.42088
Cahill, Jameson; Casazza, Peter G.; Kutyniok, Gitta
8
2013
Compressed sensing for finite-valued signals. Zbl 1370.94153
Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz E.
8
2017
The Zak transform on certain locally compact groups. Zbl 1079.43009
Kutyniok, Gitta
7
2002
Efficient resolution of anisotropic structures. Zbl 1317.65251
Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit
7
2014
Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197
Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit
7
2018
Clustered sparsity and separation of cartoon and texture. Zbl 1280.42036
Kutyniok, Gitta
7
2013
The modern mathematics of deep learning. Zbl 1520.68165
Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
7
2023
The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Zbl 1383.42031
Kutyniok, Gitta; Paternostro, Victoria; Philipp, Friedrich
7
2017
A weak qualitative uncertainty principle for compact groups. Zbl 1031.43003
Kutyniok, Gitta
6
2003
A decomposition theorem for frames and the Feichtinger conjecture. Zbl 1155.46010
Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin; Tremain, Janet C.
6
2008
Irregular shearlet frames: Geometry and approximation properties. Zbl 1226.42030
Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q
6
2011
Density of frames and Schauder bases of windowed exponentials. Zbl 1214.42070
Heil, Christopher; Kutyniok, Gitta
5
2008
A redundant version of the Rado-Horn theorem. Zbl 1103.15001
Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin
5
2006
Shearlets and optimally sparse approximations. Zbl 1251.42008
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
5
2012
Expressivity of deep neural networks. Zbl 1523.68080
Gühring, Ingo; Raslan, Mones; Kutyniok, Gitta
5
2023
Dualizable shearlet frames and sparse approximation. Zbl 1366.65119
Kutyniok, Gitta; Lim, Wang-Q
4
2016
Parabolic molecules: Curvelets, shearlets, and beyond. Zbl 1331.42038
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
4
2014
Beurling density and shift-invariant weighted irregular Gabor systems. Zbl 1156.42311
Kutyniok, Gitta
4
2006
The local integrability condition for wavelet frames. Zbl 1101.42018
Kutyniok, Gitta
4
2006
From wavelets to shearlets and back again. Zbl 1227.65139
Kutyniok, Gitta; Sauer, Tomas
4
2008
Compressed sensing and its applications. MATHEON workshop, Berlin, Germany, December 2013. Zbl 1320.94007
4
2015
Regularization and numerical solution of the inverse scattering problem using shearlet frames. Zbl 1365.65244
Kutyniok, Gitta; Mehrmann, Volker; Petersen, Philipp C.
3
2017
Transferability of spectral graph convolutional neural networks. Zbl 1539.68305
Levie, Ron; Huang, Wei; Bucci, Lorenzo; Bronstein, Michael; Kutyniok, Gitta
3
2021
Compressed sensing and its applications. Selected papers of the third international MATHEON conference, TU Berlin, Berlin, Germany, December 4–8, 2017. Zbl 1427.94002
3
2019
Shearlets on bounded domains. Zbl 1253.42035
Kutyniok, Gitta; Lim, Wang-Q
3
2012
Shearlets: theory and applications. Zbl 1311.42091
Kutyniok, Gitta; Lim, Wang-Q; Steidl, Gabriele
3
2014
Limitations of deep learning for inverse problems on digital hardware. Zbl 1547.68682
Boche, Holger; Fono, Adalbert; Kutyniok, Gitta
2
2023
The modern mathematics of deep learning. Zbl 1520.68165
Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
7
2023
Expressivity of deep neural networks. Zbl 1523.68080
Gühring, Ingo; Raslan, Mones; Kutyniok, Gitta
5
2023
Limitations of deep learning for inverse problems on digital hardware. Zbl 1547.68682
Boche, Holger; Fono, Adalbert; Kutyniok, Gitta
2
2023
The mathematics of artificial intelligence. Zbl 1535.68295
Kutyniok, Gitta
1
2023
A theoretical analysis of deep neural networks and parametric PDEs. Zbl 07493717
Kutyniok, Gitta; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold
59
2022
Approximation spaces of deep neural networks. Zbl 1491.82017
Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix
33
2022
Deep microlocal reconstruction for limited-angle tomography. Zbl 07522506
Andrade-Loarca, Héctor; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp
2
2022
Analysis of simultaneous inpainting and geometric separation based on sparse decomposition. Zbl 07528664
Do, Van Tiep; Levie, Ron; Kutyniok, Gitta
2
2022
Numerical solution of the parametric diffusion equation by deep neural networks. Zbl 1473.35331
Geist, Moritz; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold; Kutyniok, Gitta
26
2021
The modern mathematics of deep learning. (Die moderne Mathematik des tiefen Lernens.) Zbl 07571594
Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
13
2021
\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed? Zbl 1460.94021
Genzel, Martin; Kutyniok, Gitta; März, Maximilian
11
2021
The computational complexity of understanding binary classifier decisions. Zbl 1512.68116
Wäldchen, Stephan; Macdonald, Jan; Hauch, Sascha; Kutyniok, Gitta
9
2021
Transferability of spectral graph convolutional neural networks. Zbl 1539.68305
Levie, Ron; Huang, Wei; Bucci, Lorenzo; Bronstein, Michael; Kutyniok, Gitta
3
2021
Error bounds for approximations with deep ReLU neural networks in \(W^{s , p}\) norms. Zbl 1452.41009
Gühring, Ingo; Kutyniok, Gitta; Petersen, Philipp
61
2020
Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm. Zbl 1472.94004
Andrade-Loarca, Héctor; Kutyniok, Gitta; Öktem, Ozan
2
2020
Anisotropic multiscale systems on bounded domains. Zbl 1442.42076
Grohs, Philipp; Kutyniok, Gitta; Ma, Jackie; Petersen, Philipp; Raslan, Mones
1
2020
Optimal approximation with sparsely connected deep neural networks. Zbl 1499.41029
Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
97
2019
Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography. Zbl 1416.92099
Bubba, Tatiana A.; Kutyniok, Gitta; Lassas, Matti; März, Maximilian; Samek, Wojciech; Siltanen, Samuli; Srinivasan, Vignesh
28
2019
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. Zbl 1439.35009
Andrade-Loarca, Hector; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp C.
11
2019
Compressed sensing and its applications. Selected papers of the third international MATHEON conference, TU Berlin, Berlin, Germany, December 4–8, 2017. Zbl 1427.94002
3
2019
Optimal compressive imaging of Fourier data. Zbl 1437.94043
Kutyniok, Gitta; Lim, Wang-Q
11
2018
PROMP: a sparse recovery approach to lattice-valued signals. Zbl 1408.94862
Flinth, Axel; Kutyniok, Gitta
8
2018
Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197
Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit
7
2018
Classification of edges using compactly supported shearlets. Zbl 1378.42023
Kutyniok, Gitta; Petersen, Philipp
23
2017
Compressed sensing for finite-valued signals. Zbl 1370.94153
Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz E.
8
2017
The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Zbl 1383.42031
Kutyniok, Gitta; Paternostro, Victoria; Philipp, Friedrich
7
2017
Regularization and numerical solution of the inverse scattering problem using shearlet frames. Zbl 1365.65244
Kutyniok, Gitta; Mehrmann, Volker; Petersen, Philipp C.
3
2017
Compressed sensing and its applications. Second international MATHEON conference, December 2015. Zbl 1388.94005
1
2017
ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. Zbl 1347.65203
Kutyniok, Gitta; Lim, Wang-Q; Reisenhofer, Rafael
26
2016
\(\alpha\)-Molecules. Zbl 1342.42041
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
15
2016
Cartoon approximation with \(\alpha\)-curvelets. Zbl 1359.42018
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
10
2016
Dualizable shearlet frames and sparse approximation. Zbl 1366.65119
Kutyniok, Gitta; Lim, Wang-Q
4
2016
Linear stable sampling rate: optimality of 2D wavelet reconstructions from Fourier measurements. Zbl 1331.42036
Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie
16
2015
A survey of compressed sensing. Zbl 1333.94015
Boche, Holger; Calderbank, Robert; Kutyniok, Gitta; Vybíral, Jan
13
2015
Measures of scalability. Zbl 1359.94307
Chen, Xuemei; Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Wang, Rongrong
10
2015
Gabor shearlets. Zbl 1304.42084
Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng
10
2015
Compressed sensing and its applications. MATHEON workshop, Berlin, Germany, December 2013. Zbl 1320.94007
4
2015
Parabolic molecules. Zbl 1403.42038
Grohs, Philipp; Kutyniok, Gitta
34
2014
Analysis of inpainting via clustered sparsity and microlocal analysis. Zbl 1362.94007
King, Emily J.; Kutyniok, Gitta; Zhuang, Xiaosheng
24
2014
Asymptotic analysis of inpainting via universal shearlet systems. Zbl 1307.42033
Genzel, Martin; Kutyniok, Gitta
13
2014
Geometric separation by single-pass alternating thresholding. Zbl 1357.42033
Kutyniok, Gitta
10
2014
Scalable frames and convex geometry. Zbl 1307.42029
Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich
10
2014
Efficient resolution of anisotropic structures. Zbl 1317.65251
Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit
7
2014
Parabolic molecules: Curvelets, shearlets, and beyond. Zbl 1331.42038
Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin
4
2014
Shearlets: theory and applications. Zbl 1311.42091
Kutyniok, Gitta; Lim, Wang-Q; Steidl, Gabriele
3
2014
Compressed sensing. Zbl 1336.94022
Kutyniok, Gitta
1
2014
Sparse matrices in frame theory. Zbl 1306.65082
Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob
1
2014
Finite frames. Theory and applications. Zbl 1257.42001
165
2013
Scalable frames. Zbl 1260.42023
Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Tuley, Elizabeth K.
41
2013
Microlocal analysis of the geometric separation problem. Zbl 1261.94007
Donoho, David; Kutyniok, Gitta
38
2013
Introduction to finite frame theory. Zbl 1281.42032
Casazza, Peter G.; Kutyniok, Gitta; Philipp, Friedrich
24
2013
Theory and applications of compressed sensing. Zbl 1283.94018
Kutyniok, Gitta
15
2013
Fusion frames. Zbl 1261.42048
Casazza, Peter G.; Kutyniok, Gitta
12
2013
Sparsity and spectral properties of dual frames. Zbl 1280.42026
Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob
11
2013
Operators and frames. Zbl 1289.42088
Cahill, Jameson; Casazza, Peter G.; Kutyniok, Gitta
8
2013
Clustered sparsity and separation of cartoon and texture. Zbl 1280.42036
Kutyniok, Gitta
7
2013
Shearlets. Multiscale analysis for multivariate data. Zbl 1237.42001
95
2012
Construction of compactly supported shearlet frames. Zbl 1239.42031
Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q
49
2012
Introduction to shearlets. Zbl 1251.42010
Kutyniok, Gitta; Labate, Demetrio
41
2012
Optimally sparse approximations of 3D functions by compactly supported shearlet frames. Zbl 1252.42043
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
28
2012
ShearLab: a rational design of a digital parabolic scaling algorithm. Zbl 1257.42048
Kutyniok, Gitta; Shahram, Morteza; Zhuang, Xiaosheng
22
2012
Compactly supported shearlets. Zbl 1252.42042
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
13
2012
Image separation using wavelets and shearlets. Zbl 1345.94007
Kutyniok, Gitta; Lim, Wang-Q
13
2012
Digital shearlet transforms. Zbl 1255.94021
Kutyniok, Gitta; Lim, Wang-Q; Zhuang, Xiaosheng
9
2012
Shearlets and optimally sparse approximations. Zbl 1251.42008
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
5
2012
Shearlets on bounded domains. Zbl 1253.42035
Kutyniok, Gitta; Lim, Wang-Q
3
2012
Compactly supported shearlets are optimally sparse. Zbl 1226.42031
Kutyniok, Gitta; Lim, Wang-Q
63
2011
Sparse fusion frames: existence and construction. Zbl 1264.94042
Calderbank, Robert; Casazza, Peter G.; Heinecke, Andreas; Kutyniok, Gitta; Pezeshki, Ali
26
2011
Optimally sparse frames. Zbl 1365.94059
Casazza, Peter G.; Heinecke, Andreas; Krahmer, Felix; Kutyniok, Gitta
22
2011
Sparse recovery from combined fusion frame measurements. Zbl 1365.94066
Boufounos, Petros; Kutyniok, Gitta; Rauhut, Holger
20
2011
Adaptive multiresolution analysis structures and shearlet systems. Zbl 1283.42053
Han, Bin; Kutyniok, Gitta; Shen, Zuowei
17
2011
A quantitative notion of redundancy for finite frames. Zbl 1211.42027
Bodmann, Bernhard G.; Casazza, Peter G.; Kutyniok, Gitta
15
2011
Irregular shearlet frames: Geometry and approximation properties. Zbl 1226.42030
Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q
6
2011
Mini-workshop: Shearlets. Abstracts from the mini-workshop held October 3rd – October 9th, 2010. Zbl 1235.00037
2
2010
Resolution of the wavefront set using continuous shearlets. Zbl 1169.42012
Kutyniok, Gitta; Labate, Demetrio
110
2009
Shearlet coorbit spaces and associated Banach frames. Zbl 1171.42019
Dahlke, Stephan; Kutyniok, Gitta; Steidl, Gabriele; Teschke, Gerd
87
2009
Robust dimension reduction, fusion frames, and Grassmannian packings. Zbl 1283.42046
Kutyniok, Gitta; Pezeshki, Ali; Calderbank, Robert; Liu, Taotao
44
2009
Adaptive directional subdivision schemes and shearlet multiresolution analysis. Zbl 1193.42127
Kutyniok, Gitta; Sauer, Tomas
19
2009
Fusion frames and distributed processing. Zbl 1258.42029
Casazza, Peter G.; Kutyniok, Gitta; Li, Shidong
184
2008
The uncertainty principle associated with the continuous shearlet transform. Zbl 1257.42047
Dahlke, Stephan; Kutyniok, Gitta; Maass, Peter; Sagiv, Chen; Stark, Hans-Georg; Teschke, Gerd
79
2008
Robustness of fusion frames under erasures of subspaces and of local frame vectors. Zbl 1256.94017
Casazza, Peter G.; Kutyniok, Gitta
33
2008
Beurling dimension of Gabor pseudoframes for affine subspaces. Zbl 1268.42055
Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin
17
2008
Landau’s necessary density conditions for LCA groups. Zbl 1158.43004
Gröchenig, Karlheinz; Kutyniok, Gitta; Seip, Kristian
16
2008
A decomposition theorem for frames and the Feichtinger conjecture. Zbl 1155.46010
Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin; Tremain, Janet C.
6
2008
Density of frames and Schauder bases of windowed exponentials. Zbl 1214.42070
Heil, Christopher; Kutyniok, Gitta
5
2008
From wavelets to shearlets and back again. Zbl 1227.65139
Kutyniok, Gitta; Sauer, Tomas
4
2008
Convolution and Wiener amalgam spaces on the affine group. Zbl 1161.43004
Heil, Christopher; Kutyniok, Gitta
1
2008
A new identity for Parseval frames. Zbl 1136.42308
Balan, Radu; Casazza, Peter G.; Edidin, Dan; Kutyniok, Gitta
35
2007
Affine density in wavelet analysis. Zbl 1142.42017
Kutyniok, Gitta
19
2007
The homogeneous approximation property for wavelet frames. Zbl 1133.42049
Heil, Christopher; Kutyniok, Gitta
16
2007
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames. Zbl 1118.65027
Casazza, Peter G.; Kutyniok, Gitta
12
2007
Affine density, frame bounds, and the admissibility condition for wavelet frames. Zbl 1124.42027
Kutyniok, Gitta
9
2007
Sparse multidimensional representations using anisotropic dilation and shear operators. Zbl 1099.65148
Guo, Kanghui; Kutyniok, Gitta; Labate, Demetrio
97
2006
The geometry of sets of parameters of wave packet frames. Zbl 1095.42020
Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin
23
2006
The theory of reproducing systems on locally compact abelian groups. Zbl 1113.43008
Kutyniok, Gitta; Labate, Demetrio
22
2006
A redundant version of the Rado-Horn theorem. Zbl 1103.15001
Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin
5
2006
Beurling density and shift-invariant weighted irregular Gabor systems. Zbl 1156.42311
Kutyniok, Gitta
4
2006
The local integrability condition for wavelet frames. Zbl 1101.42018
Kutyniok, Gitta
4
2006
Wilson bases for general time-frequency lattices. Zbl 1090.94008
Kutyniok, Gitta; Strohmer, Thomas
12
2005
Frames of subspaces. Zbl 1058.42019
Casazza, Peter G.; Kutyniok, Gitta
239
2004
...and 10 more Documents
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Cited by 1,757 Authors

58 Kutyniok, Gitta
39 Casazza, Peter George
34 Grohs, Philipp
28 Labate, Demetrio
28 Li, Yunzhang
25 Arefijamaal, Ali Akbar
23 Petersen, Philipp Christian
20 Leng, Jinsong
20 Sun, Wenchang
19 Voigtlaender, Felix
18 Kamyabi-Gol, Rajab Ali
17 Vashisht, Lalit Kumar
16 Rahimi, Asghar
15 Bodmann, Bernhard G.
15 Guo, Kanghui
15 Han, Deguang
14 Führ, Hartmut
14 Okoudjou, Kasso A.
14 Shah, Firdous Ahmad
13 Adcock, Ben
13 Fickus, Matthew C.
13 Jentzen, Arnulf
13 Mixon, Dustin G.
13 Schwab, Christoph
13 Xiao, Xiangchun
13 Zhu, Yucan
13 Zhuang, Xiaosheng
12 Balazs, Peter
12 De Vito, Ernesto
12 Hansen, Anders C.
12 Steidl, Gabriele
11 Christensen, Ole
11 Dahlke, Stephan
11 Li, Dongwei
11 Lim, Wang-Q
11 Massey, Pedro G.
11 Stojanoff, Demetrio
10 Ahmadi, Reza H.
10 Aldroubi, Akram
10 Cabrelli, Carlos A.
10 Kaushik, Shiv Kumar
10 Teschke, Gerd
10 Xiang, Zhongqi
9 Asgari, Mohammad Sadegh
9 De Mari, Filippo
9 Deepshikha
9 Feichtinger, Hans Georg
9 Jørgensen, Palle E. T.
9 Lemvig, Jakob
9 Li, Pengtong
9 Powell, Alexander M.
9 Rahimlou, Gholamreza
9 Ruiz, Mariano A.
9 Shamsabadi, Mitra
8 Czaja, Wojciech
8 Farashahi, Arash Ghaani
8 Gabardo, Jean-Pierre
8 Han, Bin
8 Jyoti
8 Khosravi, Amir
8 Pfander, Götz E.
8 Sadri, Vahid
8 Schönlieb, Carola-Bibiane
8 Speegle, Darrin M.
7 Chen, Xuemei
7 Gröchenig, Karlheinz
7 Huang, Ting-Zhu
7 Jakobsen, Mads Sielemann
7 Javanshiri, Hossein
7 King, Emily Jeannette
7 Luef, Franz
7 Manzoni, Andrea
7 Mirzaee Azandaryani, Morteza
7 Mishra, Siddhartha
7 Neyshaburi, Fahimeh Arabyani
7 Shen, Zuowei
7 Sun, Qiyu
7 Tantary, Azhar Y.
7 Raisi Tousi, Reihaneh
7 Vera, Daniel J.
7 Wu, Zhiyi
6 Alberti, Giovanni S.
6 Benedetto, John Joseph
6 Bhandari, Animesh
6 Bubba, Tatiana A.
6 Dehghan, Mohammad Ali
6 Haas, John I. IV
6 Häuser, Sören
6 Heil, Christopher E.
6 Jasper, John Sahayam
6 Krahmer, Felix
6 Larson, David Royal
6 Levie, Ron
6 Maass, Peter
6 Öktem, Ozan
6 Raslan, Mones
6 Rauhut, Holger
6 Tran, Tin T.
6 Tremain, Janet C.
6 Waldron, Shayne F. D.
...and 1,657 more Authors
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Cited in 297 Serials

132 Applied and Computational Harmonic Analysis
72 The Journal of Fourier Analysis and Applications
57 International Journal of Wavelets, Multiresolution and Information Processing
51 Journal of Mathematical Analysis and Applications
40 Linear Algebra and its Applications
40 Advances in Computational Mathematics
30 Journal of Pseudo-Differential Operators and Applications
22 Numerical Functional Analysis and Optimization
21 Journal of Functional Analysis
21 SIAM Journal on Imaging Sciences
20 Results in Mathematics
19 Inverse Problems
19 Constructive Approximation
18 Neural Networks
18 Analysis and Applications (Singapore)
18 Sahand Communications in Mathematical Analysis
16 Linear and Multilinear Algebra
16 Journal of Approximation Theory
15 Mediterranean Journal of Mathematics
14 Proceedings of the American Mathematical Society
14 SIAM Journal on Scientific Computing
12 Journal of Inequalities and Applications
11 Journal of Computational and Applied Mathematics
11 Acta Applicandae Mathematicae
11 Foundations of Computational Mathematics
11 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
10 Complex Analysis and Operator Theory
9 Journal of Mathematical Physics
9 Journal of Scientific Computing
9 The Journal of Geometric Analysis
9 SIAM Journal on Mathematical Analysis
9 Acta Mathematica Sinica. English Series
9 Sampling Theory, Signal Processing, and Data Analysis
8 Computers & Mathematics with Applications
8 Applied Mathematics and Computation
8 Transactions of the American Mathematical Society
8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
8 Journal of Mathematical Imaging and Vision
8 Annals of Functional Analysis
7 Applicable Analysis
7 Journal of Computational Physics
7 Rocky Mountain Journal of Mathematics
7 Advances in Mathematics
7 Mathematische Nachrichten
7 SIAM Journal on Mathematics of Data Science
6 Computer Methods in Applied Mechanics and Engineering
6 Mathematics of Computation
6 Monatshefte für Mathematik
6 Bulletin of the Iranian Mathematical Society
6 Acta Numerica
6 Oberwolfach Reports
6 Science China. Mathematics
5 Mathematical Methods in the Applied Sciences
5 Journal of Complexity
5 Advances in Applied Clifford Algebras
5 Sampling Theory in Signal and Image Processing
5 Journal of Physics A: Mathematical and Theoretical
5 Communications in Computational Physics
5 Operators and Matrices
5 Journal of Mathematical Inequalities
5 Palestine Journal of Mathematics
4 Indian Journal of Pure & Applied Mathematics
4 Collectanea Mathematica
4 Mathematics and Computers in Simulation
4 Memoirs of the American Mathematical Society
4 SIAM Journal on Numerical Analysis
4 Circuits, Systems, and Signal Processing
4 Applied Mathematics Letters
4 SIAM Review
4 Integral Transforms and Special Functions
4 Abstract and Applied Analysis
4 Journal of Machine Learning Research (JMLR)
4 Inverse Problems and Imaging
4 Analysis and Mathematical Physics
4 Problemy Analiza. Issues of Analysis
4 Journal of Mathematics
4 SIAM/ASA Journal on Uncertainty Quantification
4 Journal of Linear and Topological Algebra
4 Wavelets and Linear Algebra
4 Korean Journal of Mathematics
4 SN Partial Differential Equations and Applications
3 The Annals of Statistics
3 Advances in Applied Mathematics
3 Multidimensional Systems and Signal Processing
3 Japan Journal of Industrial and Applied Mathematics
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Expositiones Mathematicae
3 Georgian Mathematical Journal
3 Opuscula Mathematica
3 Mathematical Problems in Engineering
3 Mathematical Inequalities & Applications
3 Infinite Dimensional Analysis, Quantum Probability and Related Topics
3 GAMM-Mitteilungen
3 Banach Journal of Mathematical Analysis
3 Asian-European Journal of Mathematics
3 Advances in Pure and Applied Mathematics
3 International Journal of Nonlinear Analysis and Applications
3 Journal of Function Spaces
3 Research in the Mathematical Sciences
3 Advances in Operator Theory
...and 197 more Serials
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Cited in 55 Fields

947 Harmonic analysis on Euclidean spaces (42-XX)
326 Numerical analysis (65-XX)
286 Information and communication theory, circuits (94-XX)
283 Functional analysis (46-XX)
268 Computer science (68-XX)
181 Approximations and expansions (41-XX)
149 Operator theory (47-XX)
99 Abstract harmonic analysis (43-XX)
79 Partial differential equations (35-XX)
70 Linear and multilinear algebra; matrix theory (15-XX)
66 Statistics (62-XX)
48 Topological groups, Lie groups (22-XX)
47 Operations research, mathematical programming (90-XX)
38 Biology and other natural sciences (92-XX)
36 Integral transforms, operational calculus (44-XX)
34 Quantum theory (81-XX)
32 Combinatorics (05-XX)
31 Probability theory and stochastic processes (60-XX)
21 Convex and discrete geometry (52-XX)
20 Number theory (11-XX)
19 Measure and integration (28-XX)
19 Calculus of variations and optimal control; optimization (49-XX)
16 Group theory and generalizations (20-XX)
14 Real functions (26-XX)
13 Fluid mechanics (76-XX)
13 Systems theory; control (93-XX)
12 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
10 Functions of a complex variable (30-XX)
10 Global analysis, analysis on manifolds (58-XX)
8 General and overarching topics; collections (00-XX)
8 Mechanics of deformable solids (74-XX)
7 Order, lattices, ordered algebraic structures (06-XX)
7 Special functions (33-XX)
7 Dynamical systems and ergodic theory (37-XX)
7 Geometry (51-XX)
6 Algebraic geometry (14-XX)
6 Potential theory (31-XX)
6 Statistical mechanics, structure of matter (82-XX)
5 Several complex variables and analytic spaces (32-XX)
5 Ordinary differential equations (34-XX)
5 Integral equations (45-XX)
4 Commutative algebra (13-XX)
4 Difference and functional equations (39-XX)
4 Differential geometry (53-XX)
4 General topology (54-XX)
4 Manifolds and cell complexes (57-XX)
3 Optics, electromagnetic theory (78-XX)
2 Associative rings and algebras (16-XX)
2 Mechanics of particles and systems (70-XX)
2 Geophysics (86-XX)
2 Mathematics education (97-XX)
1 History and biography (01-XX)
1 \(K\)-theory (19-XX)
1 Sequences, series, summability (40-XX)
1 Astronomy and astrophysics (85-XX)

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