Veröffentlichungen
Monographie
•
A Mathematical Introduction to Compressive Sensing.
Applied and Numerical Harmonic Analysis, Birkhäuser, 2013
Vgl. auch: Liste der Errata HTML
Buchbeiträge
•
Tensor Completion in Hierarchical Tensor Representations
In: Compressed Sensing and Its Applications, editors: H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral,
pages 419-450, Springer 2015 PDF
•
Cosparsity in Compressed Sensing
In: Compressed Sensing and Its Applications, editors: H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral,
pages 315-339, Springer, 2015 PDF
•
Compressive Sensing.
In O. Scherzer, editor, Handbook of Mathematical Methods in Imaging,
pages 187-228. Springer, 2011. PDF
•
Compressive Sensing and Structured Random Matrices.
In M. Fornasier, editor, Theoretical Foundations and Numerical Methods for Sparse Recovery,
volume 9 of Radon Series Comp. Appl. Math., pages 1-92. deGruyter, 2010. PDF
Preprints
7.
6.
Convergence of gradient descent for learning linear neural networks
Preprint, 2021
arXiv:2108.02040 [cs.LG] PDF
5.
Gradient Descent for Deep Matrix Factorization: Dynamics and Implicit Bias towards Low Rank
Preprint, 2020
arXiv:2011.13772 [cs.LG] PDF
4.
3.
A Quotient Property for Matrices with Heavy-Tailed Entries and its Application to Noise-Blind Compressed Sensing
Preprint, 2018
arXiv:1806.04261 [math.PR] PDF
2.
1.
Multi-level Compressed Sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs
Preprint, 2017
arXiv:1701.01671 [math.NA] PDF
Zeitschriftenartikel
58.
Covariance Estimation under One-bit Quantization
The Annals of Statistics 50(6):3538-3562, 2022
doi:10.1214/22-AOS2239, arXiv:2104.01280 [cs.IT] PDF
57.
More is Less: Inducing Sparsity via Overparameterization
Information and Inference, to appear
doi:10.1093/imaiai/iaad012, arXiv:2112.11027 [math.OC] PDF
56.
Path classification by stochastic linear recurrent neural networks
Advances in Discrete and Continuous Models 13, 2022
doi:10.1186/s13662-022-03686-9, arXiv:2108.03090 [stat.ML] PDF
55.
Overparameterization and generalization error: weighted trigonometric interpolation
SIAM Journal on Mathematics of Data Science 4(2), 2022
doi:10.1137/21M1390955, arXiv:2006.08495 [CS.LG] PDF
54.
Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs
Applied and Computational Harmonic Analysis 53:231-269, 2021.
doi:10.1016/j.acha.2021.01.004, arXiv:2005.06994 [cs.IT] PDF
53.
On the geometry of polytopes generated by heavy-tailed random vectors
Communications in Contemporary Mathematics, vol. 24, no. 3, 2150056, 2022
doi:10.1142/S0219199721500565, arXiv:1907.07258 [math.PR] PDF
52.
Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers
Information and Inference, Volume 11, Issue 1, 2022, Pages 307–353
doi:10.1093/imaiai/iaaa039, arXiv:1910.05505 [math.OC] PDF
51.
Tensor theta norms and low rank recovery
Numerical Algorithms 88:25-66, 2021
doi:10.1007/s11075-020-01029-x, arXiv:1505.05175 [math.IT] PDF
50.
Jointly Low-Rank and Bisparse Recovery: Questions and Partial Answers
Analysis and Applications 18(1):25-48, 2020.
49.
One-bit compressed sensing with partial Gaussian circulant matrices
Information and Inference 9(3):601-626, 2020.
doi:10.1093/imaiai/iaz017, arXiv:1710.03287 [math.IT] PDF
48.
Improved bounds for sparse recovery from subsampled random convolutions
Annals of Applied Probability 28(6):3491-3527, 2018.
doi:10.1214/18-AAP1391, arXiv:1610.04983 [math.IT] PDF
47.
Low-rank matrix recovery via rank one tight frame measurements
Journal of Fourier Analysis and Applications 25:588-593, 2019.
doi:10.1007/s00041-017-9579-x, arXiv:1612.03108 [math.IT] PDF
46.
Low rank tensor recovery via iterative hard thresholding
Linear Algebra and Its Applications 523:220-262, 2017.
45.
Stable low rank matrix recovery via null space properties
Information and Inference 5(4):405-441, 2016.
doi:10.1093/imaiai/iaw014, arXiv:1507.07184 [math.IT] PDF
44.
On the gap between restricted isometry properties and sparse recovery conditions
IEEE Trans. Inform. Theory 64(8):5478 - 5487, 2018.
doi:10.1109/TIT.2016.2570244, arXiv:1504.05073 [math.IT] PDF
43.
Refined analysis of sparse MIMO radar
Journal of Fourier Analysis and Applications 23(3):485-529, 2017.
doi:10.1007/s00041-016-9477-7, arXiv:1509.03625 [math.IT] PDF
42.
Conjugate gradient acceleration of iteratively re-weighted least squares methods
Computational Optimization and Applications 65:205-259, 2016.
41.
Uniform recovery of fusion frame structured sparse signals
Applied and Computational Harmonic Analysis 41(2):341-361, 2016.
40.
Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations
Mathematics of Computation 86(304):661-700, 2017.
doi:10.1090/mcom/3113, arXiv:1410.4929 [math.NA] PDF
39.
Low rank matrix recovery from rank one measurements
Applied and Computational Harmonic Analysis 42(1):88-116, 2017.
doi:10.1016/j.acha.2015.07.007, arXiv:1410.6913 [math.IT] PDF
38.
Robust analysis l1-recovery from Gaussian measurements and total variation minimization
European Journal of Applied Mathematics 26(06):917-929, 2015.
37.
Interpolation via weighted l1 minimization
Applied and Computational Harmonic Analysis 40(2):321-351, 2016.
doi:10.1016/j.acha.2015.02.003, arXiv:1308.0759 [math.FA] PDF
36.
Analysis l1-recovery with frames and Gaussian measurements
Acta Applicandae Mathematicae 140(1):173:195, 2015.
35.
Fast and RIP-optimal transforms.
Discrete and Computational Geometry 52(4):780-798, 2014
34.
Structured Random Measurements in Signal Processing
GAMM Mitteilungen 37(2):217-238, 2014
33.
Remote sensing via l1-minimization.
Found. Comp. Math. 14:115-150, 2014
32.
Nonuniform sparse recovery with subgaussian matrices.
Electronic Transactions on Numerical Analysis 41:167-178, 2014 PDF
31.
Suprema of chaos processes and the restricted isometry property.
Comm. Pure Appl. Math. 67(11):1877-1904, 2014
30.
The restricted isometry property for time-frequency structured random matrices.
Prob. Theory Rel. Fields 156:707-737, 2013.
29.
Sparse Legendre expansions via l1-minimization.
J. Approx. Theory, 164(5):517-533, 2012.
28.
Restricted isometries for partial random circulant matrices.
Appl. Comput. Harmonic Anal., 32(2):242-254, 2012.
27.
Sparse recovery from combined fusion frame measurements.
IEEE Trans. Inform. Theory, 57(6):3864-3876, 2011.
26.
Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type.
J. Funct. Anal., 260(11):3299-3362, 2011.
doi:10.1016/j.jfa.2010.12.006, arXiv:1010.0607 [math.FA] PDF
25.
Low-rank matrix recovery via iteratively reweighted least squares minimization.
SIAM J. Optimization, 21(4):1614-1640, 2011.
doi:10.1137/100811404, arXiv:1010.2471 [math.NA] PDF
24.
Sparsity in time-frequency representations.
J. Fourier Anal. Appl., 16(2):233-260, 2010.
doi:10.1007/s00041-009-9086-9, arXiv:0711.2503 [math.CA] PDF
23.
Compressive estimation of doubly selective channels:
exploiting channel sparsity to improve spectral efficiency in multicarrier transmissions.
IEEE Journal of Selected Topics in Signal Processing, 4(2):255-271, 2010.
22.
Average case analysis of multichannel sparse recovery using convex relaxation.
IEEE Trans. Inform. Theory, 56(1):505-519, 2010.
21.
The Gelfand widths of lp-balls for 0 < p <=1.
J. Complexity, 26:629-640, 2010. Best Paper Award 2010 of the Journal of Complexity.
doi:10.1016/j.jco.2010.04.004, arXiv:1002.0672 [math.FA] PDF
20.
Generalized Coorbit Theory, Banach Frames, and the Relation to alpha-Modulation Spaces.
Proc. London Math. Soc. (3), 96:464-506, 2008.
19.
Recovery algorithms for vector valued data with joint sparsity constraints.
SIAM J. Numer. Anal., 46(2):577-613, 2008.
18.
Iterative thresholding algorithms.
Appl. Comput. Harmon. Anal., 25(2):187-208, 2008.
17.
Atoms of all channels, unite!
Average case analysis of multi-channel sparse recovery using greedy algorithms.
J. Fourier Anal. Appl., 14(5):655-687, 2008.
16.
Random sampling of sparse trigonometric polynomials II -
orthogonal matching pursuit versus basis pursuit.
Found. Comput. Math., 8(6):737-763, 2008.
15.
Identification of matrices having a sparse representation.
IEEE Trans. Signal Process., 56(11):5376-5388, 2008.
14.
Stability results for random sampling of sparse trigonometric polynomials.
IEEE Trans. Information Theory, 54(12):5661-5670, 2008.
13.
On the impossibility of uniform sparse reconstruction using greedy methods.
Sampl. Theory Signal Image Process., 7(2):197-215, 2008. PDF
12.
Compressed sensing and redundant dictionaries.
IEEE Trans. Inform. Theory, 54(5):2210-2219, 2008.
doi:10.1109/TIT.2008.920190, arXiv:0701131 [math.PR] PDF
11.
Random sampling of sparse trigonometric polynomials.
Appl. Comput. Harmon. Anal., 22(1):16-42, 2007.
10.
Coorbit Space Theory for Quasi-Banach Spaces.
Studia Math., 180(3):237-253, 2007. PDF
9.
Wiener amalgam spaces with respect to quasi-Banach spaces.
Colloq. Math., 109(2):345-362, 2007. PDF
8.
Generalized hypergroups and orthogonal polynomials.
J. Aust. Math. Soc., 82(3):369-393, 2007. PDF
7.
Radial Time-Frequency Analysis and Embeddings of Radial Modulation Spaces.
Sampl. Theory Signal Image Process., 5(2):201-224, 2006. PDF
6.
Continuous Frames, Function Spaces, and the Discretization Problem.
J. Fourier Anal. Appl., 11(3):245-287, 2005.
5.
Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups.
Appl. Comput. Harmon. Anal., 18(1):94-122, 2005.
4.
Wavelet transforms associated to group representations and functions invariant under symmetry groups.
Int. J. Wavelets Multiresolut. Inf. Process., 3(2):167-188, 2005.
3.
Best time localized trigonometric polynomials and wavelets.
Adv. Comput. Math., 22(1):1-20, 2005.
2.
Radial multiresolution in dimension three.
Constr. Approx., 22(2):167-188, 2005.
1.
On the connection of uncertainty principles for functions on the circle and on the real line.
J. Fourier Anal. Appl., 9(4):387-409, 2003.
Konferenzbeiträge
22.
A Riemannian gradient flow perspective on learning deep linear neural networks
NeurIPS 2020 Workshop on Differential Geometry meets Deep Learning PDF
21.
Unfolding recurrence by Green's functions for optimized reservoir computing
Proc. 34th Conference on Neural Information Processing Systems (NeurIPS 2020)
arXiv:2010.06247 [stat.ML] PDF
20.
Polyhedral Sampling Structures for Phaseless Spherical Near-Field Antenna Measurements
Proc. Annual 42nd Antenna Measurement Techniques Association Symposium (AMTA) 2020
19.
Sparse recovery in MIMO radar - dependence on the support structure
Proc. CoSeRa 2015.
18.
Compressed sensing Petrov-Galerkin approximations for parametric PDEs.
Proc. SampTA'15, 2015. PDF
17.
On the minimal number of measurements in low-rank matrix recovery.
Proc. SampTA2015, 2015. PDF
16.
Analysis of low rank matrix recovery via Mendelson’s small ball method.
Proc. SampTA2015, 2015. PDF
15.
Recovery of third order tensors via convex optimization
Proc. SampTA2015, 2015. PDF
14.
Analysis of Sparse Recovery in MIMO Radar
Proc. SampTA2015, 2015. PDF
13.
Nonuniform sparse recovery with fusion frames.
Proc. SPARS'13, 2013. PDF
12.
Low rank tensor tensor recovery via iterative hard thresholding.
Proc. SampTA 2013. PDF
11.
Recovery of cosparse signals with Gaussian measurements.
Proc. SampTA 2013. PDF
10.
Sparse recovery with fusion frames via RIP
Proc. SampTA 2013. PDF
9.
Recovery of functions of many variables via compressive sensing.
Proc. SampTA 2011. PDF
8.
Sparse recovery for spherical harmonic expansions.
Proc. SampTA 2011. PDF
7.
Sparse and Low Rank Recovery.
Oberwolfach Reports, volume 7, pages 1990-1993, 2010. PDF
6.
Multichannel-compressive estimation of doubly selective channels in MIMO-OFDM systems: Exploiting and enhancing joint sparsity.
Proc. IEEE ICASSP 2010, Dallas, 2010.
5.
Average case analysis of sparse recovery from combined fusion frame measurements.
Proc. CISS 2010, Princeton, 2010. PDF
4.
Average case analysis of multichannel basis pursuit.
Proc. SampTA09, Marseille, France, 2009. PDF
3.
Circulant and Toeplitz matrices in compressed sensing.
Proc. SPARS'09, Saint-Malo, France, 2009. PDF
2.
Identification of sparse operators.
Oberwolfach Reports 36:2130-2133, 2007. PDF
1.
Average case analysis of multichannel thresholding
Proc. ICASSP 07, Hawaii, 2007 PDF