Edit Profile (opens in new tab) Kutyniok, Gitta Co-Author Distance Author ID: kutyniok.gitta Published as: Kutyniok, Gitta Homepage: https://www.ai.math.uni-muenchen.de/members/professor/kutyniok/index.html External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Twitter · dblp · GND · IdRef Videos: carmin.tv Documents Indexed: 123 Publications since 1998, including 2 Books and 10 Additional arXiv Preprints 21 Contributions as Editor Software Indexed: 2 Packages Co-Authors: 136 Co-Authors with 125 Joint Publications 4,543 Co-Co-Authors 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 all top 5 Fields 87 Harmonic analysis on Euclidean spaces (42-XX) 63 Information and communication theory, circuits (94-XX) 55 Numerical analysis (65-XX) 38 Computer science (68-XX) 20 General and overarching topics; collections (00-XX) 17 Approximations and expansions (41-XX) 13 Functional analysis (46-XX) 11 Partial differential equations (35-XX) 11 Abstract harmonic analysis (43-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 8 Operator theory (47-XX) 8 Operations research, mathematical programming (90-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications 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. 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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. 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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 all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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