Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence
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Journal Publications

2021

  • M. Geist, P. Petersen, M. Raslan, R. Schneider, and G. Kutyniok. Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. J. Sci. Comput., to appear (arXiv:2004.12131). 
  • R. Levie, C. Yapar, G. Kutyniok, and G. Caire. RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks. IEEE T. Wirel. Commun., Early Access Publication (DOI: 10.1109/TWC.2021.3054977). [pdf]
  • R. Gribonval, G. Kutyniok, M. Nielsen, and F. Voigtlaender. Approximation spaces of deep neural networks. Constr. Approx., to appear (arXiv:1905.01208). [pdf]
  • V. Tiep Do, R. Levie, and G. Kutyniok. Analysis of simultaneous inpainting and geometric separation based on sparse decomposition. Anal. Appl., to appear (arXiv:2009.09398). 
  • G. Kutyniok, P. Petersen, M. Raslan, and R. Schneider. A Theoretical Analysis of DeepNeural Networks and Parametric PDEs. Constr. Approx., to appear (arXiv:1904.00377). 
  • M. Genzel, G. Kutyniok and M. März. l_1-Analysis Minimization and Generalized (Co-) Sparsity: When Does Recovery Succeed? Appl. Comput. Harmon. Anal. 52 (2021), 82-140 (arXiv:1710.04952). 
  • S. Wäldchen, J. Macdonald, S. Hauch, and G. Kutyniok. The Computational Complexity of Understanding Network Decisions. J. Artif. Intell. Res. 70 (2021), 351-387.  [pdf]

2020

  • H. Andrade-Loarca, G. Kutyniok, and O. Öktem. Shearlets as Feature Extractor for Semantic Edge Detection: The Model-Based and Data-Driven Realm. P. Roy. Soc. A 476 (2020), Article ID:20190841. [pdf]
  • P. Grohs, G. Kutyniok, J. Ma, P. Petersen, and M. Raslan. Anisotropic Multiscale Systems on Bounded Domains. Adv. Comput. Math. 46 (2020), Article No.: 39. [pdf]
  • G. Kutyniok. Discussion of "Nonparametric regression using deep neural networks with ReLU activation function". Ann. Stat. 48 (2020), 1902–1905. 
  • I. Gühring, G. Kutyniok, and P. Petersen. Error bounds for approximations with deep ReLU neural networks in Ws,pnorms. Anal. Appl. 18 (2020), 803–859. 

2019

  • F. Sureau, F. Voigtlaender, M. Wust, J.-L. Starck, and G. Kutyniok. Learning sparse representations on the sphere. Astron. Astrophys. 621 (2019), A73 (arXiv:1809.10437).
  • H. Bölcskei, P. Grohs, G. Kutyniok, and P. Petersen. Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM J. Math. Data Sci. 1 (2019), 8–45. [pdf]
  • T. A. Bubba, G. Kutyniok, M. Lassas, M. März, W. Samek, S. Siltanen, and V. Srinivasan. Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography. Inverse Probl. 35, 2019.  [pdf]
  • H. Andrade-Loarca, G. Kutyniok, O. Öktem, and P. Petersen. Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. SIAM J. Imaging Sci. 12 (2019), 1936–1966. [pdf]

2018

  • A. Flinth and G. Kutyniok. PROMP: A Sparse Recovery Approach to Lattice-Valued Signals. Appl. Comput. Harmon. Anal. 45 (2018), 668–708. [pdf]
  • R. Reisenhofer, S. Bosse, G. Kutyniok, and T. Wiegand. A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment. Signal Proc. Image Comm. 61 (2018), 33–43. [pdf]
  • G. Kutyniok and W.-Q Lim. Optimal Compressive Imaging of Fourier Data. SIAM J. Imaging Sci. 11 (2018), 507–546. [pdf]
  • W. Dahmen, W.-Q Lim, G. Kutyniok, C. Schwab, and G. Welper. Adaptive Anisotropic Petrov-Galerkin Methods for First Order Transport Equations. J. Comput. Appl. Math. 340 (2018), 191–220. [pdf]
  • J. Ma, M. März, S. Funk, J. Schulz-Menger, G. Kutyniok, T. Schaeffter, and C. Kol- bitsch. Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting. Phys. Med. Biol. 63 (2018), 235004 (arXiv:1705.00463). 

2017

  • G. Kutyniok and P. Petersen. Classification of Edges using Compactly Supported Shearlets. Appl. Comput. Harmon. Anal. 42 (2017), 245–293 (arXiv:1411.5657).
  • G. Kutyniok, V. Mehrmann, and P. Petersen. Regularization and Numerical Solution of the Inverse Scattering Problem Using Shearlet Frames. J. Inverse Ill-Posed Probl. 25 (2017), 287–309 (arXiv:1407.7349).
  • G. Kutyniok, V. Paternostro, and F. Philipp. The Effect of Perturbations of Frame Sequences and Fusion Frames on Their Duals. Oper. Matrices 11 (2017), 301–336 (arXiv:1509.04160).
  • T. Conrad, N. Cvetkovic, M. Genzel, G. Kutyniok, C. Schtte, J. Vybiral, and N. Wulkow. Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data. BMC Bioinformatics 18 (2017), 160–180 (arXiv:1506.03620).
  • S. Keiper, G. Kutyniok, D. G. Lee, and G. E. Pfander. Compressed Sensing for Finite-Valued Signals. Linear Algebra Appl. 532 (2017), 570–613 (arXiv:1609.09450).

2016

  • G. Kutyniok, W.-Q Lim, and R. Reisenhofer. ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets. ACM Trans. Math. Software 42 (2016), Article No.: 5 (arXiv:1402.5670).
  • P. Grohs, S. Keiper, G. Kutyniok, and M. Schäfer. α-Molecules. Appl. Comput. Harmon. Anal. 41 (2016), 297–336 (arXiv:1407.4424).
  • G. Kutyniok and W.-Q Lim. Dualizable Shearlet Frames and Sparse Approximation. Constr. Approx. 44 (2016), 53–86 (arXiv:1411.2303).
  • D. Mücke-Herzberg, P. Abellan, M. Sarahan, I. Godfrey, Z. Saghi, R. Leary, A. Stevens, J. Ma, G. Kutyniok, F. Azough, R. Freer, P. Midgley, N. Browning, and Q. Ramasse. Practical Implementation of Compressive Sensing for High Resolution STEM. Microsc. Microanal. 22(S3) (2016), 558–559.
  • P. Grohs, S. Keiper, G. Kutyniok, and M. Schäfer. Cartoon Approximation with α-Curvelets. J. Fourier Anal. Appl. 22 (2016), 1235–1293 (arXiv:1404.1043).

2015

  • B. Bodmann, G. Kutyniok, and X. Zhuang. Gabor Shearlets. Appl. Comput. Harmon. Anal. 38 (2015), 87–114 (arXiv:1303.6556).
  • B. Adcock, A. C. Hansen, G. Kutyniok, and J. Ma. Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. SIAM J. Math. Anal. 47 (2015), 1196–1233 (arXiv:1403.0172).
  • X. Chen, G. Kutyniok, K. A. Okoudjou, F. Philipp, and R. Wang. Measures of Scalability. IEEE Trans. Inform. Theory 61 (2015), 4410–4423 (arXiv:1406.2137).
  • H. Lakshman, W.-Q Lim, H. Schwarz, D. Marpe, G.Kutyniok, and T. Wiegand. Image interpolation using Shearlet based iterative refinement. Signal Proc. Image Comm. 36 (2015), 83–94 (arXiv:1308.1126).

2014

  • G. Kutyniok. Geometric Separation by Single-Pass Alternating Thresholding. Appl. Comput. Harmon. Anal. 36 (2014), 23–50 (arXiv:1204.6120).
  • E. J. King, G. Kutyniok, and X. Zhuang. Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis. J. Math. Imaging Vis. 48 (2014), 205–234 (arXiv:1206.2526).
  • P. Grohs and G. Kutyniok. Parabolic Molecules. Found. Comput. Math. 14 (2014), 299–337 (arXiv:1206.1958).
  • F. Krahmer, G. Kutyniok, and J. Lemvig. Sparse Matrices in Frame Theory. Comput. Stat. 29 (2014), 547–568. [pdf]
  • M. Genzel and G. Kutyniok. Asymptotic Analysis of Inpainting via Universal Shearlet Systems. SIAM J. Imaging Sci. 7 (2014), 2301–2339 (arXiv:1405.3747).

2013

  • D. L. Donoho and G. Kutyniok. Microlocal Analysis of the Geometric Separation Problem. Comm. Pure Appl. Math. 66 (2013), 1–47 (arXiv:1004.3006).
  • G. Kutyniok, K. A. Okoudjou, F. Philipp, and E. K. Tuley. Scalable Frames. Linear Algebra Appl. 438 (2013), 2225–2238 (arXiv:1204.1880).
  • G. Kutyniok. Clustered Sparsity and Separation of Cartoon and Texture. SIAM J. Imaging Sci. 6 (2013), 848–874 (arXiv:1204.6123).
  • F. Krahmer, G. Kutyniok, and J. Lemvig. Sparsity and spectral properties of dual frames. Linear Algebra Appl. 439 (2013), 982–998 (arXiv:1204.5062).
  • J. Cahill, P. G. Casazza, and G. Kutyniok. Operators and Frames. J. Operat. Theor. 70 (2013), 145–164. [pdf]

2012

  • P. Kittipoom, G. Kutyniok, and W.-Q Lim. Construction of Compactly Supported Shearlets. Constr. Approx. 35 (2012), 21–72 (arXiv:1003.5481).
  • G. Kutyniok, J. Lemvig, and W.-Q Lim. Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames. SIAM J. Math. Anal. 44 (2012), 2962–3017 (arXiv:1109.5993).
  • G. Kutyniok, M. Shahram, and X. Zhuang. ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm. SIAM J. Imaging Sci. 5 (2012), 1291–1332 (arXiv:1106.1319).

2011

  • B. G. Bodmann, P. G. Casazza, and G. Kutyniok. A Quantitative Notion of Redundancy for Finite Frames. Appl. Comput. Harmon. Anal. 30 (2011), 348–362 (arXiv:0910.5904).
  • R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. Sparse Fusion Frames: Existence and Construction. Adv. Comput. Math. 35 (2011), 1–31. [pdf]
  • B. Boufounos, G. Kutyniok, and H. Rauhut. Sparse Recovery from Combined Fusion Frame Measurements. IEEE Trans. Inform. Theory 57 (2011), 3864–3876. [pdf]
  • P. Kittipoom, G. Kutyniok, and W.-Q Lim. Irregular Shearlet Frames: Geometry and Approximation Properties. J. Fourier Anal. Appl. 17 (2011), 604–639.  [pdf]
  • G. Kutyniok and W.-Q Lim. Compactly Supported Shearlets are Optimally Sparse. J. Approx. Theory 163 (2011), 1564–1589 (arXiv:1002.2661).
  • B. Han, G. Kutyniok, and Z. Shen. Adaptive Multiresolution Analysis Structures and Shearlet Systems. SIAM J. Numer. Anal. 49 (2011), 1921–1946. [pdf]
  • P. G. Casazza, A. Heinecke, F. Krahmer, and G. Kutyniok. Optimally Sparse Frames. IEEE Trans. Inform. Theory 57 (2011), 7279–7287 (arXiv:1009.3663).

2009

  • G. Kutyniok, A. Pezeshki, A. R. Calderbank, and T. Liu. Robust Dimension Reduction, Fusion Frames, and Grassmannian Packings. Appl. Comput. Harmon. Anal. 26 (2009), 64–76 (arXiv:0709.2340).
  • G. Kutyniok and D. Labate. Resolution of the wavefront set using continuous shearlets. Trans. Amer. Math. Soc. 361 (2009), 2719–2754. [pdf]
  • G. Kutyniok and T. Sauer. Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis. SIAM J. Math. Anal. 41 (2009), 1436–1471 (arXiv:0710.2678).
  • S. Dahlke, G. Kutyniok, G. Steidl, and G. Teschke. Shearlet Coorbit Spaces and associated Banach Frames. Appl. Comput. Harmon. Anal. 27 (2009), 195–214. [pdf]

2008

  •  P. G. Casazza, G. Kutyniok, D. Speegle, and J. C. Tremain. A Decomposition Theorem for frames and the Feichtinger Conjecture. Proc. Amer. Math. Soc. 136 (2008), 2043–2053 (arXiv:math/0702216).
  • W. Czaja, G. Kutyniok, and D. Speegle. Beurling dimension of Gabor pseudo frames of affine subspaces. J. Fourier Anal. Appl. 14 (2008), 514–537. [pdf]
  • P. G. Casazza, G. Kutyniok, and S. Li. Fusion frames and distributed processing. Appl. Comput. Harmon. Anal. 25 (2008), 114–132 (arXiv:math/0605374).
  • S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, and G. Teschke. The uncertainty principle associated with the continuous shearlet transform. Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), 157–181. [pdf]
  • C. Heil and G. Kutyniok. Density of frames and Schauder bases of windowed exponentials. Houston J. Math. 34 (2008), 565–600. [pdf]
  • K. Grc╠łhenig, G. Kutyniok, and K. Seip. Landau’s necessary density conditions for LCA groups. J. Funct. Anal. 255 (2008), 1831–1850 (arXiv:0803.3529).

2007

  • G. Kutyniok and D. Labate. Construction of Regular and Irregular Shearlet Frames. J. Wavelet Theory and Appl. 1 (2007), 1–10.
  • R. Balan, P.G. Casazza, D. Edidin, and G. Kutyniok. A fundamental identity for Parseval frames. Proc. Amer. Math. Soc. 135 (2007), 1007–1015 (arXiv:math/0506357).
  • G. Kutyniok. Affine density, frame bounds, and the admissibility condition for wavelet frames. Constr. Approx. 25 (2007), 239–253. [pdf]
  • P.G. Casazza and G. Kutyniok. A generalization of Gram-Schmidt orthogonalization generating all Parseval frames. Adv. Comput. Math. 27 (2007), 65–78. [pdf]
  • C. Heil and G. Kutyniok. The Homogeneous Approximation Property for Wavelet Frames. J. Approx. Theory 147 (2007), 28–46. [pdf]

2006

  • W. Czaja, G. Kutyniok, and D. Speegle. The geometry of the parameters of wave packet frames. Appl. Comput. Harmon. Anal. 20 (2006), 108–125. [pdf]
  • G. Kutyniok. The local integrability condition for wavelet frames. J. Geom. Anal. 16 (2006), 155–166. [pdf]
  • G. Kutyniok. Beurling density and shift-invariant weighted irregular Gabor systems. Sampl. Theory Signal Image Process. 5 (2006), 131–149. [pdf]
  • P.G. Casazza, G. Kutyniok, and D. Speegle. A redundant version of the Rado-Horn Theorem. Linear Algebra Appl. 418 (2006), 1–10. [pdf]
  • G. Kutyniok and D. Labate. The theory of reproducing systems on locally compact abelian groups. Colloq. Math. 106 (2006), 197–220. [pdf]

2005

  • G. Kutyniok and T. Strohmer. Wilson bases for general time-frequency lattices. SIAM J. Math. Anal. 37 (2005), 685–711. [pdf]

2004

  • P.G. Casazza, G. Kutyniok, and M.C. Lammers. Duality principles in Frame Theory. J. Fourier Anal. Appl. 10 (2004), 383–408. [pdf]

2003

  • G. Kutyniok. Ambiguity functions, Wigner distributions and Cohen’s class for LCA groups. J. Math. Anal. Appl. 277 (2003), 589–608. [pdf]
  • C. Heil and G. Kutyniok. Density of weighted wavelet frames. J. Geom. Anal. 13 (2003), 479–493. [pdf]
  • G. Kutyniok. A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups. J. Math. Anal. Appl. 279 (2003), 580–596. [pdf]
  • G. Kutyniok. A weak qualitative uncertainty principle for compact groups. Illinois J. Math. 47 (2003), 709–724. [pdf]

2002

  • G. Kutyniok. Linear independence of time-frequency shifts under a generalized Schrödinger representation. Arch. Math. 78 (2002), 135–144. [pdf]
  • G. Kutyniok. The Zak transform on certain locally compact groups. J. of Math. Sciences 1 (2002), 62–85. [pdf]
  • K. Gröchenig, D. Han, C. Heil, and G. Kutyniok. The Balian-Low theorem for symplectic lattices in higher dimensions. Appl. Comput. Harmon. Anal. 13 (2002), 169–176. [pdf]

1998

  • E. Kaniuth and G. Kutyniok. Zeros of the Zak transform on locally compact abelian groups. Proc. Amer. Math. Soc. 126 (1998), 3561–3569. [pdf]