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TU Berlin

Inhalt des Dokuments

Forschung

Forschungsschwerpunkte
Angewandte Harmonische Analysis
Compressed Sensing
Data Science
Deep Learning
Frame Theorie
Hoch-dimensionale Datenanalyse
Imaging Science
Inverse Probleme
Numerik von partielle Differentialgleichungen
Sparse Approximation
Anwendungen in der Signal- und Bildverarbeitung (Medizin, Telekommunikation,...)
Forschungswebseiten
Webadresse
Inhalt
www.shearlet.org
Einleitung und Publikationen zu Shearlettheorie
www.shearlab.org
Softwarepakete zur Shearlettransformation

Compressed Sensing, Sparsity und l_1 Minimierung

Compressed Sensing, Sparsity und l_1 Minimierung
Nr.
Titel
25
S. Keiper, G. Kutyniok, D. Lee, and G. Pfander.
Reconstruction of finite-valued sparse signals.
Wavelets and Sparsity XVII (San Diego, CA, 2017), 1039415, SPIE Proc. 10394, SPIE, Bellingham, WA, 2017.
Download (PDF, 762,8 KB)
24
G. Kutyniok and W.-Q Lim.
Optimal Compressive Imaging of Fourier Data.
Submitted (2015).
Download (PDF, 523,8 KB)
23
A. Flinth and G. Kutyniok.
PROMP: A Sparse Recovery Approach to Lattice-Valued Signals.
Appl. Comput. Harmon. Anal., to appear.
Download (PDF, 1,0 MB)
22
S. Keiper, G. Kutyniok, D. G. Lee, and G. E. Pfander.
Compressed Sensing for Finite-Valued Signals.
Linear Algebra Appl. 532 (2017), 570-613.
Download (PDF, 1,1 MB)
21
T. Conrad, N. Cvetkovic, M. Genzel, G. Kutyniok, C. Schütte, 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. 
Download (PDF, 1,011,4 KB)
20
A. Flinth, A. Hashemi, and G. Kutyniok.
Compressed Sensing: From Theory to Praxis.

Compressive Sensing of Earth Observations (C.H. Chen, ed.), Taylor and Francis, 2017.
19
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.
18
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.
A Compressive Sensing based acquisition design for quantitative ultra-low dose high-resolution imaging and spectroscopy in the STEM.
Proceedings of the European Microscopy Congress, 2016.
17
H. Boche, R. Calderbank, G. Kutyniok and J. Vybiral.
Compressed Sensing and its Applications: MATHEON Workshop 2013
Birkhäuser Boston, 2015.
16
H. Boche, R. Calderbank, G. Kutyniok, and J. Vybiral.
A Survey of Compressed Sensing.
Compressed Sensing and its Applications, 1-40, Birkhäuser Boston, 2015.
Download (PDF, 300,4 KB)
15
G. Kutyniok.
Compressed Sensing.
DMV Mitteilungen 22 (2014), 24-29.
Download (PDF, 669,0 KB)
14
H. Lakshman, W.-Q Lim, H. Schwarz, D. Marpe, G. Kutyniok, and T. Wiegand.
Image Interpolation using Shearlet Based Sparsity Priors.
ICIP'13 (Melbourne, Australia, 2013), Proc., 655-659, IEEE, 2013.
Download (PDF, 708,7 KB)
13
G. Kutyniok.
Theory and Applications of Compressed Sensing.
GAMM Mitteilungen 36 (2013), 79-101.
Download (PDF, 811,4 KB)
12
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. 
Download (PDF, 615,2 KB)
11
G. Kutyniok.
Geometric Separation by Single-Pass Alternating Thresholding.
Appl. Comput. Harmon. Anal. 36 (2014), 23-50.
Download (PDF, 376,7 KB)
10
G. Kutyniok.
Clustered Sparsity and Separation of Cartoon and Texture.
SIAM J. Imaging Sci. 6 (2013), 848–874.
Download (PDF, 334,4 KB)
9
D. L. Donoho and G. Kutyniok.
Microlocal Analysis of the Geometric Separation Problem.
Comm. Pure Appl. Math. 66 (2013), 1-47.
Download (PDF, 489,2 KB)
8
Y. Eldar and G. Kutyniok.
Compressed Sensing: Theory and Applications
Cambridge University Press, 2012.
Link zu Amazon
7
M. Davenport, M. Duarte, Y. Eldar, and G. Kutyniok.
Introduction to Compressed Sensing.
Compressed Sensing: Theory and Applications, 1-64, Cambridge University Press, 2012.
Download (PDF, 819,1 KB)
6
G. Kutyniok.
Data Separation by Sparse Representations.
Compressed Sensing: Theory and Applications, 485-514, Cambridge University Press, 2012.
Download (PDF, 937,4 KB)
5
E. J. King, G. Kutyniok, and X. Zhuang.
Analysis of Data Separation and Recovery Problems using Clustered Sparsity.
Wavelets and Sparsity XIV (San Diego, CA, 2009), 813818-1 - 813818-11, SPIE Proc. 8138, SPIE, Bellingham, WA, 2011.
Download (PDF, 130,0 KB)
4
B. Boufounos, G. Kutyniok, and H. Rauhut.
Sparse Recovery from Combined Fusion Frame Measurements.
IEEE Trans. Inform. Theory 57 (2011), 3864-3876.
Download (PDF, 393,4 KB)
3
P. Boufounos, G. Kutyniok, and H. Rauhut.
Compressed Sensing for Fusion Frames.
Wavelets XIII (San Diego, CA, 2009), 744614-1 - 744614-11, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
Download (PDF, 179,9 KB)
2
D. L. Donoho and G. Kutyniok.
Geometric Separation using a Wavelet-Shearlet Dictionary.
SampTA'09 (Marseille, France, 2009), Proc., 2009.
Download (PDF, 125,8 KB)
1
D. L. Donoho and G. Kutyniok.
Analysis of l_1 Minimization in the Geometric Separation Problem.
42nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2008), 274-279.
Download (PDF, 164,2 KB)

Data Science/Deep Learning/Hoch-dimensionale Datananalyse

Data Science/Deep Learning/Hoch-dimensionale Datananalyse
Nr.
Title
4
H. Bölcskei, P. Grohs, G. Kutyniok, and P. Petersen.
Memory-Optimal Neural Network Approximation.
Wavelets and Sparsity XVII (San Diego, CA, 2017), 103940Q, SPIE Proc. 10394, SPIE, Bellingham, WA, 2017.
Download (PDF, 369,7 KB)
3
H. Bölcskei, P. Grohs, G. Kutyniok, and P. Petersen.
Optimal Approximation with Sparsely Connected Deep Neural Networks.
Submitted (2017).
Download (PDF, 577,5 KB)
2
M. Genzel and G. Kutyniok.
A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations.
Submitted (2016).
Download (PDF, 471,4 KB)
1
T. Conrad, N. Cvetkovic, M. Genzel, G. Kutyniok, C. Schütte, 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.
Download (PDF, 1,011,4 KB)

Frame Theorie

Frame Theorie
Nr.
Titel
40
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.
Download (PDF, 407,0 KB)
39
G. Kutyniok, V. Paternostro, and F. Philipp.
Perturbations of Fusion Frames and the Effect on Their Canonical Dual.
Wavelets and Sparsity XVI (San Diego, CA, 2015), 95970S-95977S, SPIE Proc. 9597, SPIE, Bellingham, WA, 2015.
Download (PDF, 292,3 KB)
38
X. Chen, G. Kutyniok, K. A. Okoudjou, F. Philipp, and R. Wang.
Measures of Scalability.
IEEE Trans. Inform. Theory 61 (2015), 4410-4423.
Download (PDF, 466,1 KB)
37
G. Kutyniok, K. Okoudjou, and F. Philipp.
Scalable Frames and Convex Geometry.
Spectra of Wavelets, Tilings, and Frames (Boulder, CO, 2012), Contemp. Math. 345, 19-32, Amer. Math. Soc., Providence, RI, 2013.
Download (PDF, 339,0 KB)
36
H. Boche, M. Guillemard, G. Kutyniok, and F. Philipp.
Signal Recovery from Thresholded Frame Measurements.
Wavelets and Sparsity XV (San Diego, CA, 2013), D88580-1-D88580-7, SPIE Proc. 8858, SPIE, Bellingham, WA, 2013.
Download (PDF, 278,6 KB)
35
G. Kutyniok, K. A. Okoudjou, and F. Philipp.
Preconditioning of Frames.
Wavelets and Sparsity XV (San Diego, CA, 2013), G88580-1-G88580-8, SPIE Proc. 8858, SPIE, Bellingham, WA, 2013.
Download (PDF, 98,7 KB)
34
G.Kutyniok.
Fusion Frames and Wireless Sensor Networks.
IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), to appear.
Download (PDF, 187,6 KB)
33
F. Krahmer, G. Kutyniok, and J. Lemvig.
Spectral properties of dual frames.
10th International Conference on Sampling Theory and Applications (Bremen, Germany, 2013), 493-496, Eurasip, 2013.
Download (PDF, 300,8 KB)
32
H. Boche, M. Guillemard, G. Kutyniok, and F. Philipp.
Signal Analysis with Frame Theory and Persistent Homology.
10th International Conference on Sampling Theory and Applications (Bremen, Germany, 2013), 309-331, Eurasip, 2013.
Download (PDF, 585,1 KB)
31
G. Kutyniok, K. Okoudjou and F. Philipp.
Perfect Preconditioning of Frames by a Diagonal Operator.
10th International Conference on Sampling Theory and Applications (Bremen, Germany, 2013), 85--88, Eurasip, 2013.
Download (PDF, 66,6 KB) 
30
F. Krahmer, G. Kutyniok, and J. Lemvig.
Sparse Matrices in Frame Theory.
Comput.Stat. 29 (2014), 547-568.
Download (PDF, 142,5 KB)
29
J. Cahill, P. G. Casazza, and G. Kutyniok.
Operators and Frames.
J. Operat. Theor. 70 (2013), 145-164.
Download (PDF, 176,9 KB)
28
F. Krahmer, G. Kutyniok, and J. Lemvig.
Sparsity and spectral properties of dual frames.
Linear Algebra Appl. 439 (2013), 982-998.
Download (PDF, 300,8 KB)
27
G. Kutyniok, K. A. Okoudjou, F. Philipp, and E. K. Tuley.
Scalable Frames.
Linear Algebra Appl. 438 (2013), 2225–2238.
Download (PDF, 640,8 KB)
26
P. G. Casazza and G. Kutyniok.
Fusion Frames.
Finite Frames: Theory and Applications, 437-478, Birkhäuser Boston, 2012.
Download (PDF, 332,2 KB)
25
P. G. Casazza, G. Kutyniok, and F. Philipp.
Introduction to Finite Frame Theory.
Finite Frames: Theory and Applications, 1-53, Birkhäuser Boston, 2012.
Download (PDF, 289,9 KB)
24
P. G. Casazza and G. Kutyniok.
Finite Frames: Theory and Applications.
Birkhäuser Boston, 2012.
Link zu Amazon
23
B. G. Bodmann, P. G. Casazza, and G. Kutyniok.
A Quantitative Notion of Redundancy and its Applications.
SampTA'11 (Singapore, 2011), Proc., 2011.
Download (PDF, 70,4 KB)
22
P. G. Casazza, A. Heinecke, and G. Kutyniok.
Optimally Sparse Fusion Frames: Existence and Construction.
SampTA'11 (Singapore, 2011), Proc., 2011.
Download (PDF, 187,0 KB)
21
P. G. Casazza, A. Heinecke, F. Krahmer, and G. Kutyniok.
Optimally Sparse Frames.
IEEE Trans. Inform. Theory 57 (2011), 7279-7287.
Download (PDF, 135,7 KB)
20
B. Boufounos, G. Kutyniok, and H. Rauhut.
Sparse Recovery from Combined Fusion Frame Measurements.
IEEE Trans. Inform. Theory 57 (2011), 3864-3876.
Download (PDF, 393,4 KB)
19
B. Boufounos, G. Kutyniok, and H. Rauhut.
Average Case Analysis of Sparse Recovery from Combined Fusion Frame Measurements.
43nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2010), to appear.
Download (PDF, 103,8 KB)
18
B. G. Bodmann, P. G. Casazza, and G. Kutyniok.
Upper and Lower Redundancy of Finite Frames.
43nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2010), to appear.
Download (PDF, 89,0 KB)
17
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.
Download (PDF, 246,2 KB)
16
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.
Download (PDF, 228,7 KB)
15
B. G. Bodmann and G. Kutyniok.
Erasure-Proof Transmissions: Fusion Frames meet Coding Theory.
Wavelets XIII (San Diego, CA, 2009), 74460P-1 - 74460P-11, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
Download (PDF, 189,1 KB)
14
B. G. Bodmann, P. G. Casazza, G. Kutyniok, and S. Senger.
A Low Complexity Replacement Scheme for Erased Frame Coefficients.
Wavelets XIII (San Diego, CA, 2009), 74460O-1 - 74460O-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
Download (PDF, 171,9 KB)
13
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki.
Constructing Fusion Frames with Desired Parameters.
Wavelets XIII (San Diego, CA, 2009), 744612-1 - 744612-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
Download (PDF, 153,4 KB)
12
B. G. Bodmann, G. Kutyniok and A. Pezeshki.
Erasure-Proof Coding with Fusion Frames.
SampTA'09 (Marseille, France, 2009), Proc., 2009.
Download (PDF, 67,9 KB)
11
B. G. Bodmann, P. G. Casazza, G. Kutyniok, and S. Senger.
Error Correction for Erasures of Quantized Frame Coefficients.
SampTA'09 (Marseille, France, 2009), Proc., 2009.
Download (PDF, 50,4 KB)
10
A. Pezeshki, G. Kutyniok, and A. R. Calderbank.
Fusion frames and Robust Dimension Reduction.
42nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2008), 264-268.
Download (PDF, 71,8 KB)
9
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.
Download (PDF, 209,7 KB)
8
P. G. Casazza and G. Kutyniok.
Robustness of Fusion Frames under Erasures of Subspaces and of Local Frame Vectors.
Radon transforms, geometry, and wavelets (New Orleans, LA, 2006), 149-160, Contemp. Math. 464, Amer. Math. Soc., Providence, RI, 2008.
Download (PDF, 211,2 KB)
7
P. G. Casazza, G. Kutyniok, and S. Li.
Fusion Frames and Distributed Processing.
Appl. Comput. Harmon. Anal. 25 (2008), 114-132.
Download (PDF, 272,7 KB)
6
P. G. Casazza, G. Kutyniok, S. Li, and C. J. Rozell.
Modeling Sensor Networks with Fusion Frames.
Wavelets XII (San Diego, CA, 2007), 67011M-1 - 67011M-11, SPIE Proc. 6701, SPIE, Bellingham, WA, 2007.
Download (PDF, 179,8 KB)
5
P.G. Casazza and G. Kutyniok.
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames.
Adv. Comput. Math. 27 (2007), 65-78.
Download (PDF, 153,6 KB)
4
R. Balan, P.G. Casazza, D. Edidin, and G. Kutyniok.
A new identity for Parseval frames.
Proc. Amer. Math. Soc. 135 (2007), 1007-1015.
Download (PDF, 127,5 KB)
3
R. Balan, P.G. Casazza, D. Edidin, and G. Kutyniok.
Decompositions of frames and a new frame identity.
Wavelets XI (San Diego, CA, 2005), 379-388, SPIE Proc. 5914, SPIE, Bellingham, WA, 2005.
Download (PDF, 120,2 KB)
2
P.G. Casazza, G. Kutyniok, and M.C. Lammers.
Duality principles in frame theory.
J. Fourier Anal. Appl. 10 (2004), 383-408.
Download (PDF, 289,8 KB)
1
P.G. Casazza and G. Kutyniok.
Frames of subspaces.
Wavelets, Frames and Operator Theory (College Park, MD, 2003), 87-113, Contemp. Math. 345, Amer. Math. Soc., Providence, RI, 2004.
Download (PDF, 322,8 KB)

Geometric Multiscale Analysis

Geometric Multiscale Analysis
Nr.
Titel
39
J. Ma, M. März, S. Funk, J. Schulz-Menger, G. Kutyniok, T. Schaeffter, and C. Kolbitsch.
Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting.
Submitted (2017).
Download (PDF, 2,5 MB)
38
G. Kutyniok and W.-Q Lim.
Optimal Compressive Imaging of Fourier Data.
Submitted (2015).
Download (PDF, 523,8 KB)
37
P. Grohs, S. Keiper, G. Kutyniok, and M. Schäfer.
Cartoon Approximation with $\alpha$-Curvelets.
J. Fourier Anal. Appl. 22 (2016), 1235-1293.
Download (PDF, 724,3 KB)
36
G. Kutyniok and W.-Q Lim.
Dualizable Shearlet Frames and Sparse Approximation.
Constr. Approx. 44 (2016), 53-86.
Download (PDF, 290,3 KB)
35
P. Grohs, S. Keiper, G. Kutyniok, and M. Schäfer.
$\alpha$-Molecules.
Appl. Comput. Harmon. Anal. 41 (2016), 297-336.
Download (PDF, 752,8 KB)
34
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.
Download (PDF, 1,5 MB)
33
G. Kutyniok, W.-Q Lim, and G. Steidl.
Shearlets: Theory and Applications.
GAMM-Mitteilungen 37 (2014), 259-280.
Download (PDF, 1,2 MB)
32
G. Kutyniok.
Geometric Multiscale Analysis: From Wavelets to Parabolic Molecules.
Int. Math. Nachrichten 225 (2014), 1-16.
Download (PDF, 188,2 KB)
31
P. Grohs, S. Keiper, G. Kutyniok, and M. Schäfer.
Parabolic Molecules: Curvelets, Shearlets, and Beyond.
Approximation Theory XIV (San Antonio, TX, 2013), 141-172, Springer Proc. Math., 2014.
Download (PDF, 332,2 KB)
30
S. Keiper, G.Kutyniok, P. Grohs, and M. Schäfer.
Alpha-Molecules: Curvelets, Shearlets, Ridgelets, and Beyond.
Wavelets and Sparsity XV (San Diego, CA, 2013), 885804-1-885804-12, SPIE Proc. 8858, SPIE, Bellingham, WA, 2013.
Download (PDF, 198,5 KB)
29
B. Bodmann, G. Kutyniok, and X. Zhuang.
Gabor Shearlets.
Appl. Comput. Harmon. Anal. 38 (2015), 87-114.
Download (PDF, 196,9 KB)
28
P. Grohs and G. Kutyniok.
Parabolic Molecules.
Found. Comput. Math. 14 (2014), 299-337.
Download (PDF, 460,3 KB)
27
B. G. Bodmann, G. Kutyniok, and X. Zhuang.
Coarse Quantization with the Fast Digital Shearlet Transform.
Wavelets and Sparsity XIV (San Diego, CA, 2011), 8138OZ-1 - 8138OZ-10, SPIE Proc. 8138, SPIE, Bellingham, WA, 2011.
Download (PDF, 312,7 KB)
26
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.
Download (PDF, 1,0 MB)
25
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.
Download (PDF, 1,0 MB)
24
P. Kittipoom, G. Kutyniok, and Wang-Q Lim.
Construction of Compactly Supported Shearlet Frames.
Constr. Approx. 35 (2012), 21-72.
Download (PDF, 402,3 KB)
23
B. Han, G. Kutyniok, and Z. Shen.
Adaptive Multiresolution Analysis Structures and Shearlet Systems.
SIAM J. Numer. Anal. 49 (2011), 1921-1946.
Download (PDF, 637,7 KB)
22
G. Kutyniok and D. Labate.
Introduction to Shearlets.
Shearlets: Multiscale Analysis for Multivariate Data, 1-38, Birkhäuser Boston, 2012.
Download (PDF, 401,7 KB)
21
G. Kutyniok and D. Labate.
Shearlets: Multiscale Analysis for Multivariate Data
Birkhäuser Boston, 2012.
Link zu Amazon
20
G. Kutyniok, J. Lemvig, and W.-Q Lim.
Shearlets and Optimally Sparse Approximations.
Shearlets: Multiscale Analysis for Multivariate Data, 145-198, Birkhäuser Boston, 2012.
Download (PDF, 952,8 KB)
19
G. Kutyniok, W.-Q Lim, and X. Zhuang.
Digital Shearlet Transforms.
Shearlets: Multiscale Analysis for Multivariate Data, 239-282, Birkhäuser Boston, 2012.
Download (PDF, 690,0 KB)
18
G. Kutyniok and Wang-Q Lim.
Image Separation using Wavelets and Shearlets.
Curves and Surfaces (Avignon, France, 2010), Lecture Notes in Computer Science 6920, 416-430, Springer, 2012.
Download (PDF, 723,8 KB)
17
G. Kutyniok, J. Lemvig, and W.-Q Lim.
Optimally Sparse Approximations of Multivariate Functions Using Compactly Supported Shearlet Frames.
SampTA'11 (Singapore, 2011), Proc., 2011.
Download (PDF, 235,6 KB)
16
D. L. Donoho, G. Kutyniok, M. Shahram, and X. Zhuang.
A Rational Design of a Digital Shearlet Transform.
SampTA'11 (Singapore, 2011), Proc., 2011.
Download (PDF, 207,8 KB)
15
G. Kutyniok and Wang-Q Lim.
Compactly Supported Shearlets are Optimally Sparse
J. Approx. Theory 163 (2011), 1564-1589.
Download (PDF, 191,0 KB)
14
P. Kittipoom, G. Kutyniok, and Wang-Q Lim.
Irregular Shearlet Frames: Geometry and Approximation Properties.
J. Fourier Anal. Appl. 17 (2011), 604-639.
Download (PDF, 367,4 KB)
13
G. Kutyniok, J. Lemvig, and W.-Q Lim.
Compactly Supported Shearlets.
Approximation Theory XIII (San Antonio, TX, 2010), Springer Proc. Math. 13, 163-186, Springer, 2012.
Download (PDF, 1,8 MB)
12
G. Kutyniok and W.-Q Lim.
Shearlets on Bounded Domains.
Approximation Theory XIII (San Antonio, TX, 2010), Springer Proc. Math. 13, 187-206, Springer, 2012.
Download (PDF, 186,9 KB)
11
G. Kutyniok and Demetrio Labate.
Shearlets: The First Five Years.
Oberwolfach Report 44 (2010), 1-5.
10
G. Kutyniok, M. Shahram, and D. L. Donoho.
Development of a Digital Shearlet Transform Based on Pseudo-Polar FFT.
Wavelets XIII (San Diego, CA, 2009), 74460B-1 - 74460B-13, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
Download (PDF, 358,9 KB)
9
G. Kutyniok and T. Sauer.
Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis.
SIAM J. Math. Anal. 41 (2009), 1436-1471.
Download (PDF, 598,7 KB)
8
S. Dahlke, G. Kutyniok, G. Steidl, and G. Teschke.
Shearlet Coorbit Spaces and associated Banach Frames.
Appl. Comput. Harmon. Anal. 27 (2009), 195-214.
Download (PDF, 1,1 MB)
7
G. Kutyniok and D. Labate.
Resolution of the Wavefront Set using Continuous Shearlets.
Trans. Amer. Math. Soc. 361 (2009), 2719-2754.
Download (PDF, 364,0 KB)
6
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.
Download (PDF, 468,6 KB)
5
G. Kutyniok and T. Sauer.
From Wavelets to Shearlets and back again.
Approximation Theory XII (San Antonio, TX, 2007), Nashboro Press, Nashville, TN (2008), 201-209.
Download (PDF, 344,1 KB)
4
G. Kutyniok.
Shearlets: A Wavelet-Based Approach to the Detection of Directional Features.
Oberwolfach Report 36 (2007), 35-38.
3
G. Kutyniok and D. Labate.
Construction of Regular and Irregular Shearlet Frames.
J. Wavelet Theory and Appl. 1 (2007), 1-10.
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2
K. Guo, G. Kutyniok, and D. Labate.
Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators.
Wavelets and Splines (Athens, GA, 2005), Nashboro Press, Nashville, TN (2006), 189-201.
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1
D. Labate, W-Q. Lim, G. Kutyniok, and G. Weiss.
Sparse multidimensional representation using shearlets.
Wavelets XI (San Diego, CA, 2005), 254-262, SPIE Proc. 5914, SPIE, Bellingham, WA, 2005.
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Imaging Sciences

Imaging Sciences
Nr.
Titel
22
R. Reisenhofer, S. Bosse, G. Kutyniok, and T. Wiegand.
A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment.
Submitted (2016).
Download (PDF, 2,9 MB)
Download Code (M, 4,7 KB)
21
G. Kutyniok and W.-Q Lim.
Optimal Compressive Imaging of Fourier Data.
Submitted (2015).
Download (PDF, 523,8 KB)
20
G. Kutyniok, M. März, and J. Ma.
Mathematical Methods in Medical Image Processing.
Quantification of Biophysical Parameters by Medical Imaging (I. Sack and T. Schäffter, eds.), Springer, 2017.
19
G. Kutyniok and P. Petersen.
Classification of Edges using Compactly Supported Shearlets.
Appl. Comput. Harmon. Anal. 42 (2017), 245-293.
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18
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.
Download (PDF, 1,4 MB)
17
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.
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16
M. Genzel and G. Kutyniok.
Asymptotic Analysis of Inpainting via Universal Shearlet Systems.
SIAM J. Imaging Sci. 7 (2014), 2301-2339.
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15
E. King, G.Kutyniok, and W.-Q Lim
Image Inpainting: Theoretical Analysis and Comparison of Algorithms.
Wavelets and Sparsity XV (San Diego, CA, 2013), 885802-1-885802-11, SPIE Proc. 8858, SPIE, Bellingham, WA, 2013.
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14
H. Lakshman, W.-Q Lim, H. Schwarz, D. Marpe, G. Kutyniok, and T. Wiegand.
Image Interpolation using Shearlet Based Sparsity Priors.
ICIP'13 (Melbourne, Australia, 2013), Proc., 655--659, IEEE, 2013.
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13
B. G. Bodmann, G. Kutyniok, and X. Zhuang.
Coarse Quantization with the Fast Digital Shearlet Transform.
Wavelets and Sparsity XIV (San Diego, CA, 2011), 8138OZ-1 - 8138OZ-10, SPIE Proc. 8138, SPIE, Bellingham, WA, 2011.
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12
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.
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11
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.
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10
B. Han, G. Kutyniok, and Z. Shen.
Adaptive Multiresolution Analysis Structures and Shearlet Systems.
SIAM J. Numer. Anal. 49 (2011), 1921-1946.
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9
G. Kutyniok, W.-Q Lim, and X. Zhuang.
Digital Shearlet Transforms.
Shearlets: Multiscale Analysis for Multivariate Data, 239-282, Birkhäuser Boston, 2012.
Download (PDF, 690,0 KB)
8
G. Kutyniok and Wang-Q Lim.
Image Separation using Wavelets and Shearlets.
Curves and Surfaces (Avignon, France, 2010), Lecture Notes in Computer Science 6920, 416-430Springer, 2012.
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7
D. L. Donoho, G. Kutyniok, M. Shahram, and X. Zhuang.
A Rational Design of a Digital Shearlet Transform.
SampTA'11 (Singapore, 2011), Proc., 2011.
Download (PDF, 207,8 KB)
6
G. Kutyniok and Wang-Q Lim.
Compactly Supported Shearlets are Optimally Sparse
J. Approx. Theory 163 (2011), 1564-1589.
Download (PDF, 191,0 KB)
5
G. Kutyniok and W.-Q Lim.
Shearlets on Bounded Domains.
Approximation Theory XIII (San Antonio, TX, 2010), Springer Proc. Math. 13, 187-206, Springer, 2012.
Download (PDF, 186,9 KB)
4
G. Kutyniok, M. Shahram, and D. L. Donoho.
Development of a Digital Shearlet Transform Based on Pseudo-Polar FFT.
Wavelets XIII (San Diego, CA, 2009), 74460B-1 - 74460B-13, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.
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3
G. Kutyniok and T. Sauer.
Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis.
SIAM J. Math. Anal. 41 (2009), 1436-1471.
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2
G. Kutyniok.
Shearlets: A Wavelet-Based Approach to the Detection of Directional Features.
Oberwolfach Report 36 (2007), 35-38.
1
A. Klein, G. Kutyniok, T. Sauer, and W. Skrandies.
Wavelets in Neurophysiology.
Brain Topography 20 (2007), 52-53.
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Kadison-Singer Vermutung

Kadison-Singer Vermutung
Nr.
Titel
2
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.
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1
P.G. Casazza, G. Kutyniok, and D. Speegle.
A redundant version of the Rado-Horn Theorem.
Linear Algebra Appl. 418 (2006), 1-10.
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Partielle Differentialgleichungen

Partielle Differentialgleichungen
Nr.
Titel
4
W. Dahmen, G. Kutyniok, W.-Q Lim, C. Schwab, and G. Welper.
Adaptive Anisotropic Petrov-Galerkin Methods for First Order Transport Equations.
Submitted (2015).
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3
P. Grohs, G. Kutyniok, J. Ma, and P. Petersen.
Anisotropic Multiscale Systems on Bounded Domains.
Submitted (2015).
Download (PDF, 575,2 KB)
2
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.
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1
W. Dahmen, C. Huang, G. Kutyniok, W.-Q Lim, C. Schwab, and G. Welper.
Efficient Resolution of Anisotropic Structures.
Extraction of Quantifiable Information from Complex Systems, 25-51, Springer, 2014.
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Time-Frequency Analysis

Time-Frequency Analysis
Nr.
Titel
14
K. Gröchenig, G. Kutyniok, and K. Seip.
Landau's necessary density conditions for LCA groups.
J. Funct. Anal. 255 (2008), 1831-1850.
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13
W. Czaja, G. Kutyniok, and D. Speegle.
Beurling dimension of Gabor pseudoframes for affine subspaces.
J. Fourier Anal. Appl. 14 (2008), 514-537.
Download (PDF, 274,0 KB)
12
G. Kutyniok and C. Heil.
Density of frames and Schauder bases of windowed exponentials.
Houston J. Math. 34 (2008), 565-600.
Download (PDF, 274,3 KB)
11
G. Kutyniok.
Time/Frequency Analysis.
Human Cognitive Neurophysiology 1 (2008), 12-21.
Download (PDF, 304,7 KB)
10
G. Kutyniok.
Beurling density and shift-invariant weighted irregular Gabor systems.
Sampl. Theory Signal Image Process. 5 (2006), 163-181.
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9
G. Kutyniok and T. Strohmer.
Wilson bases for general time-frequency lattices.
SIAM J. Math. Anal. 37 (2005), 685-711.
Download (PDF, 328,4 KB)
8
P.G. Casazza, G. Kutyniok, and M.C. Lammers.
Duality principles, localization of frames, and Gabor theory.
Wavelets XI (San Diego, CA, 2005), 389-398, SPIE Proc. 5914, SPIE, Bellingham, WA, 2005.
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7
G. Ascensi and G. Kutyniok.
Accumulative density.
Wavelets XI (San Diego, CA, 2005), 188-195, SPIE Proc. 5914, SPIE, Bellingham, WA, 2005.
Download (PDF, 121,0 KB)
6
G. Kutyniok.
Ambiguity functions, Wigner distributions and Cohen's class for LCA groups.
J. Math. Anal. Appl. 277 (2003), 589-608.
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5
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.
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4
G. Kutyniok.
The Zak transform on certain locally compact groups.
J. of Math. Sciences 1 (2002), 62-85.
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3
G. Kutyniok.
Linear independence of time-frequency shifts under a generalized Schrödinger representation.
Arch. Math. 78 (2002), 135-144.
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2
G. Kutyniok.
Time-frequency analysis on locally compact groups.
Doktorarbeit, Universität Paderborn (2000).
Download (PDF, 992,4 KB)
1
E. Kaniuth and G. Kutyniok.
Zeros of the Zak transform on locally compact abelian groups.
Proc. Amer. Math. Soc. 126 (1998), 3561-3569.
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Übersichtsartikel

Übersichtsartikel
Nr.
Titel
12
G. Kutyniok.
Geometric Multiscale Analysis: From Wavelets to Parabolic Molecules.
Int. Math. Nachrichten 225 (2014), 1-16.
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11
H. Boche, R. Calderbank, G. Kutyniok, and J. Vybiral.
A Survey of Compressed Sensing.
Compressed Sensing and its Applications, 1-40, Birkhäuser Boston, 2015.
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10
G. Kutyniok.
Compressed Sensing.
DMV Mitteilungen 22 (2014), 24-29.
Download (PDF, 669,0 KB)
9
P. G. Casazza and G. Kutyniok.
Fusion Frames.
Finite Frames: Theory and Applications, 437-478, Birkhäuser Boston, 2012.
Download (PDF, 332,2 KB)
8
P. G. Casazza, G. Kutyniok, and F. Philipp.
Introduction to Finite Frame Theory.
Finite Frames: Theory and Applications, 1-53, Birkhäuser Boston, 2012.
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7
G. Kutyniok.
Theory and Applications of Compressed Sensing.
GAMM Mitteilungen 36 (2013), 79-101.
Download (PDF, 811,4 KB)
6
G. Kutyniok and D. Labate.
Introduction to Shearlets.
Shearlets: Multiscale Analysis for Multivariate Data, 1-38, Birkhäuser Boston, 2012.
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5
G. Kutyniok, J. Lemvig, and W.-Q Lim.
Shearlets and Optimally Sparse Approximations.
Shearlets: Multiscale Analysis for Multivariate Data, 145-198, Birkhäuser Boston, 2012.
Download (PDF, 952,8 KB)
4
G. Kutyniok, W.-Q Lim, and X. Zhuang.
Digital Shearlet Transforms.
Shearlets: Multiscale Analysis for Multivariate Data, 239-282, Birkhäuser Boston, 2012.
Download (PDF, 690,0 KB)
3
M. Davenport, M. Duarte, Y. Eldar, and G. Kutyniok.
Introduction to Compressed Sensing.
Compressed Sensing: Theory and Applications, 1-64, Cambridge University Press, 2012.
Download (PDF, 819,1 KB)
2
G. Kutyniok.
Data Separation by Sparse Representations.
Compressed Sensing: Theory and Applications, 485-514, Cambridge University Press, 2012.
Download (PDF, 937,4 KB)
1
G. Kutyniok.
What is Applied Harmonic Analysis?.
DMV Mitteilungen 16 (2008), 78-84.
Download (PDF, 195,9 KB)

Unschärfeprinzipien

Unschärfeprinzipien
Nr.
Titel
2
G. Kutyniok.
A weak qualitative uncertainty principle for compact groups.
Illinois J. Math. 47 (2003), 709-724.
Download (PDF, 235,6 KB)
1
G. Kutyniok.
A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups.
J. Math. Anal. Appl. 279 (2003), 580-596.
Download (PDF, 259,4 KB)

Wavelet Analysis

Wavelet Analysis
Nr.
Titel
11
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.
Download (PDF, 1,4 MB)
10
C. Heil and G. Kutyniok.
Convolution and Wiener Amalgam Spaces on the Affine Group.
Recent Advances in Computational Science (Beijing, China, 2005), World Scientific, Singapore (2008), 209-217.
Download (PDF, 112,2 KB)
9
C. Heil and G. Kutyniok.
The Homogeneous Approximation Property for Wavelet Frames.
J. Approx. Theory 147 (2007), 28-46.
Download (PDF, 207,7 KB)
8
G. Kutyniok.
Affine density in wavelet analysis.
Lecture Notes in Mathematics 1914 , Springer-Verlag, Berlin, 2007, 142 + xii pp.
ISBN: 978-3-540-72916-7
Link zu Amazon
7
G. Kutyniok.
Affine density, frame bounds, and the admissibility condition for wavelet frames.
Constr. Approx. 25 (2007), 239-253.
Download (PDF, 186,2 KB)
6
G. Kutyniok and D. Labate.
The theory of reproducing systems on locally compact abelian groups.
Colloq. Math. 106 (2006), 197-220.
Download (PDF, 234,9 KB)
5
G. Kutyniok.
The local integrability condition for wavelet frames.
J. Geom. Anal. 16 (2006), 155-166.
Download (PDF, 171,4 KB)
4
W. Czaja, G. Kutyniok, and D. Speegle.
The geometry of sets of parameters of wave packet frames.
Appl. Comput. Harmon. Anal. 20 (2006), 108-125.
Download (PDF, 197,4 KB)
3
G. Kutyniok.
Computation of the density of weighted wavelet systems.
Wavelets X (San Diego, CA, 2003), 393-404, SPIE Proc. 5207, SPIE, Bellingham, WA, 2003.
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2
C. Heil and G. Kutyniok.
Density of weighted wavelet frames.
J. Geom. Anal. 13 (2003), 479-493.
Download (PDF, 254,8 KB)
1
G. Kutyniok.
Konstruktion von stetigen und diskreten Wavelet-Transformationen auf der n-dimensionalen Sphäre mittels quadrat-integrierbarer Darstellungen.
Diplomarbeit, Universität Paderborn (1996).
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