S. Foucart, H. Rauhut

A Mathematical Introduction to Compressive Sensing.

Applied and Numerical Harmonic Analysis, Birkhäuser, 2013



H. Rauhut, R. Schneider, Z. Stojanac

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


M. Kabanava, H. Rauhut

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


M. Fornasier, H. Rauhut

Compressive Sensing.

In O. Scherzer, editor, Handbook of Mathematical Methods in Imaging,
pages 187-228. Springer, 2011. PDF


H. Rauhut

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




F. Hoppe, F. Krahmer, J. Maly, M. Menzel, H. Rauhut, C.M. Verdun

Uncertainty quantification for sparse Fourier recovery

Preprint, 2022



G. M. Nguegnang, H. Rauhut, U. Terstiege

Convergence of gradient descent for learning linear neural networks

Preprint, 2021



H.H. Chou, C. Gieshoff, J. Maly, H. Rauhut

Gradient Descent for Deep Matrix Factorization: Dynamics and Implicit Bias towards Low Rank

Preprint, 2020



A. Behboodi, H. Rauhut, E. Schnoor

Generalization bounds for deep thresholding networks

Preprint, 2020



F. Krahmer, C. Kümmerle, H. Rauhut

A Quotient Property for Matrices with Heavy-Tailed Entries and its Application to Noise-Blind Compressed Sensing

Preprint, 2018



M. Kabanava, H. Rauhut

Masked Toeplitz covariance estimation

Preprint, 2017



J.-L. Bouchot, H. Rauhut, C. Schwab

Multi-level Compressed Sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs

Preprint, 2017




S. Dirksen, J. Maly, H. Rauhut

Covariance Estimation under One-bit Quantization

The Annals of Statistics 50(6):3538-3562, 2022



H.-H. Chou, J. Maly, H. Rauhut

More is Less: Inducing Sparsity via Overparameterization

Information and Inference, to appear



W. Bartolomaeus, Y. Boutaib, S. Nestler, H. Rauhut

Path classification by stochastic linear recurrent neural networks

Advances in Discrete and Continuous Models 13, 2022



H.H. Chou, H. Rauhut, R. Ward, Y. Xie

Overparameterization and generalization error: weighted trigonometric interpolation

SIAM Journal on Mathematics of Data Science 4(2), 2022



S. Brugiapaglia, S. Dirksen, H.C. Jung, H. Rauhut

Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

Applied and Computational Harmonic Analysis 53:231-269, 2021.



O. Guédon, F. Krahmer, C. Kümmerle, S. Mendelson, H. Rauhut

On the geometry of polytopes generated by heavy-tailed random vectors

Communications in Contemporary Mathematics, vol. 24, no. 3, 2150056, 2022



B. Bah, H. Rauhut, U. Terstiege, M. Westdickenberg

Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers

Information and Inference, Volume 11, Issue 1, 2022, Pages 307–353



H. Rauhut, Z. Stojanac

Tensor theta norms and low rank recovery

Numerical Algorithms 88:25-66, 2021



S. Foucart, R. Gribonval, L. Jacques, H. Rauhut

Jointly Low-Rank and Bisparse Recovery: Questions and Partial Answers

Analysis and Applications 18(1):25-48, 2020.



S. Dirksen, H. C. Jung, H. Rauhut

One-bit compressed sensing with partial Gaussian circulant matrices

Information and Inference 9(3):601-626, 2020.



S. Mendelson, H. Rauhut, R. Ward

Improved bounds for sparse recovery from subsampled random convolutions

Annals of Applied Probability 28(6):3491-3527, 2018.



H. Rauhut, U. Terstiege

Low-rank matrix recovery via rank one tight frame measurements

Journal of Fourier Analysis and Applications 25:588-593, 2019.



H. Rauhut, R. Schneider, Z. Stojanac

Low rank tensor recovery via iterative hard thresholding

Linear Algebra and Its Applications 523:220-262, 2017.



M. Kabanava, R. Kueng, H. Rauhut, U. Terstiege

Stable low rank matrix recovery via null space properties

Information and Inference 5(4):405-441, 2016.



S. Dirksen, G. Lecué, H. Rauhut

On the gap between restricted isometry properties and sparse recovery conditions

IEEE Trans. Inform. Theory 64(8):5478 - 5487, 2018.



D. Dorsch, H. Rauhut

Refined analysis of sparse MIMO radar

Journal of Fourier Analysis and Applications 23(3):485-529, 2017.



M. Fornasier, S. Peter, H. Rauhut, S. Worm

Conjugate gradient acceleration of iteratively re-weighted least squares methods

Computational Optimization and Applications 65:205-259, 2016.



U. Ayaz, S. Dirksen, H. Rauhut

Uniform recovery of fusion frame structured sparse signals

Applied and Computational Harmonic Analysis 41(2):341-361, 2016.



H. Rauhut, C. Schwab

Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations

Mathematics of Computation 86(304):661-700, 2017.



R. Kueng, H. Rauhut, U. Terstiege

Low rank matrix recovery from rank one measurements

Applied and Computational Harmonic Analysis 42(1):88-116, 2017.



M. Kabanava, H. Rauhut, H. Zhang

Robust analysis l1-recovery from Gaussian measurements and total variation minimization

European Journal of Applied Mathematics 26(06):917-929, 2015.



H. Rauhut, R. Ward

Interpolation via weighted l1 minimization

Applied and Computational Harmonic Analysis 40(2):321-351, 2016.



M. Kabanava, H. Rauhut

Analysis l1-recovery with frames and Gaussian measurements

Acta Applicandae Mathematicae 140(1):173:195, 2015.



N. Ailon, H. Rauhut

Fast and RIP-optimal transforms.

Discrete and Computational Geometry 52(4):780-798, 2014



F. Krahmer, H. Rauhut

Structured Random Measurements in Signal Processing

GAMM Mitteilungen 37(2):217-238, 2014



M. Hügel, H. Rauhut, T. Strohmer

Remote sensing via l1-minimization.

Found. Comp. Math. 14:115-150, 2014



U. Ayaz, H. Rauhut

Nonuniform sparse recovery with subgaussian matrices.

Electronic Transactions on Numerical Analysis 41:167-178, 2014 PDF



F. Krahmer, S. Mendelson, H. Rauhut

Suprema of chaos processes and the restricted isometry property.

Comm. Pure Appl. Math. 67(11):1877-1904, 2014



G. Pfander, H. Rauhut, J. Tropp

The restricted isometry property for time-frequency structured random matrices.

Prob. Theory Rel. Fields 156:707-737, 2013.



H. Rauhut, R. Ward

Sparse Legendre expansions via l1-minimization.

J. Approx. Theory, 164(5):517-533, 2012.



H. Rauhut, J. Romberg, J. Tropp

Restricted isometries for partial random circulant matrices.

Appl. Comput. Harmonic Anal., 32(2):242-254, 2012.



P. Boufounos, G. Kutyniok, H. Rauhut

Sparse recovery from combined fusion frame measurements.

IEEE Trans. Inform. Theory, 57(6):3864-3876, 2011.



H. Rauhut, T. Ullrich

Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type.

J. Funct. Anal., 260(11):3299-3362, 2011.



M. Fornasier, H. Rauhut, R. Ward

Low-rank matrix recovery via iteratively reweighted least squares minimization.

SIAM J. Optimization, 21(4):1614-1640, 2011.



G. Pfander, H. Rauhut

Sparsity in time-frequency representations.

J. Fourier Anal. Appl., 16(2):233-260, 2010.



D. Eiwen, F. Hlawatsch, H. Rauhut, G. Tauböck

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.



Y. Eldar, H. Rauhut

Average case analysis of multichannel sparse recovery using convex relaxation.

IEEE Trans. Inform. Theory, 56(1):505-519, 2010.



S. Foucart, A. Pajor, H. Rauhut, T. Ullrich

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.



S. Dahlke, M. Fornasier, H. Rauhut, G. Steidl, G. Teschke

Generalized Coorbit Theory, Banach Frames, and the Relation to alpha-Modulation Spaces.

Proc. London Math. Soc. (3), 96:464-506, 2008.



M. Fornasier, H. Rauhut

Recovery algorithms for vector valued data with joint sparsity constraints.

SIAM J. Numer. Anal., 46(2):577-613, 2008.



M. Fornasier, H. Rauhut

Iterative thresholding algorithms.

Appl. Comput. Harmon. Anal., 25(2):187-208, 2008.



R. Gribonval, H. Rauhut, K. Schnass, P. Vandergheynst

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.



S. Kunis, H. Rauhut

Random sampling of sparse trigonometric polynomials II -
orthogonal matching pursuit versus basis pursuit.

Found. Comput. Math., 8(6):737-763, 2008.



G.E. Pfander, H. Rauhut, J. Tanner

Identification of matrices having a sparse representation.

IEEE Trans. Signal Process., 56(11):5376-5388, 2008.



H. Rauhut

Stability results for random sampling of sparse trigonometric polynomials.

IEEE Trans. Information Theory, 54(12):5661-5670, 2008.



H. Rauhut

On the impossibility of uniform sparse reconstruction using greedy methods.

Sampl. Theory Signal Image Process., 7(2):197-215, 2008. PDF



H. Rauhut, K. Schnass, P. Vandergheynst

Compressed sensing and redundant dictionaries.

IEEE Trans. Inform. Theory, 54(5):2210-2219, 2008.



H. Rauhut

Random sampling of sparse trigonometric polynomials.

Appl. Comput. Harmon. Anal., 22(1):16-42, 2007.



H. Rauhut

Coorbit Space Theory for Quasi-Banach Spaces.

Studia Math., 180(3):237-253, 2007. PDF



H. Rauhut

Wiener amalgam spaces with respect to quasi-Banach spaces.

Colloq. Math., 109(2):345-362, 2007. PDF



R. Lasser, J. Obermaier, H. Rauhut

Generalized hypergroups and orthogonal polynomials.

J. Aust. Math. Soc., 82(3):369-393, 2007. PDF



H. Rauhut

Radial Time-Frequency Analysis and Embeddings of Radial Modulation Spaces.

Sampl. Theory Signal Image Process., 5(2):201-224, 2006. PDF



M. Fornasier, H. Rauhut

Continuous Frames, Function Spaces, and the Discretization Problem.

J. Fourier Anal. Appl., 11(3):245-287, 2005.



H. Rauhut

Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups.

Appl. Comput. Harmon. Anal., 18(1):94-122, 2005.



H. Rauhut

Wavelet transforms associated to group representations and functions invariant under symmetry groups.

Int. J. Wavelets Multiresolut. Inf. Process., 3(2):167-188, 2005.



H. Rauhut

Best time localized trigonometric polynomials and wavelets.

Adv. Comput. Math., 22(1):1-20, 2005.



H. Rauhut, M. Rösler

Radial multiresolution in dimension three.

Constr. Approx., 22(2):167-188, 2005.



J. Prestin, E. Quak, H. Rauhut, K. Selig

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.




B. Bah, H. Rauhut, U. Terstiege, M. Westdickenberg

A Riemannian gradient flow perspective on learning deep linear neural networks

NeurIPS 2020 Workshop on Differential Geometry meets Deep Learning PDF



D. Dahmen, M. Gilson, C. Keup, S. Nestler, H. Rauhut

Unfolding recurrence by Green's functions for optimized reservoir computing

Proc. 34th Conference on Neural Information Processing Systems (NeurIPS 2020)



C. Culotta-Lopez, A. Guth, D. Heberling, J. Maly, H. Rauhut

Polyhedral Sampling Structures for Phaseless Spherical Near-Field Antenna Measurements

Proc. Annual 42nd Antenna Measurement Techniques Association Symposium (AMTA) 2020



D. Dorsch, H. Rauhut

Sparse recovery in MIMO radar - dependence on the support structure

Proc. CoSeRa 2015.



J.L. Bouchot, B. Bykowski, H. Rauhut, C. Schwab

Compressed sensing Petrov-Galerkin approximations for parametric PDEs.

Proc. SampTA'15, 2015. PDF



M. Kabanava, H. Rauhut, U. Terstiege

On the minimal number of measurements in low-rank matrix recovery.

Proc. SampTA2015, 2015. PDF



M. Kabanava, H. Rauhut, U. Terstiege

Analysis of low rank matrix recovery via Mendelson’s small ball method.

Proc. SampTA2015, 2015. PDF



H. Rauhut, Z. Stojanac

Recovery of third order tensors via convex optimization

Proc. SampTA2015, 2015. PDF



D. Dorsch, H. Rauhut

Analysis of Sparse Recovery in MIMO Radar

Proc. SampTA2015, 2015. PDF



U. Ayaz, H. Rauhut

Nonuniform sparse recovery with fusion frames.

Proc. SPARS'13, 2013. PDF



H. Rauhut, R. Schneider, Z. Stojanac

Low rank tensor tensor recovery via iterative hard thresholding.

Proc. SampTA 2013. PDF



M. Kabanava, H. Rauhut

Recovery of cosparse signals with Gaussian measurements.

Proc. SampTA 2013. PDF



U. Ayaz, H. Rauhut

Sparse recovery with fusion frames via RIP

Proc. SampTA 2013. PDF



A. Cohen, R. DeVore, S. Foucart, H. Rauhut

Recovery of functions of many variables via compressive sensing.

Proc. SampTA 2011. PDF



H. Rauhut, R. Ward

Sparse recovery for spherical harmonic expansions.

Proc. SampTA 2011. PDF



H. Rauhut

Sparse and Low Rank Recovery.

Oberwolfach Reports, volume 7, pages 1990-1993, 2010. PDF



N. Czink, D. Eiwen, F. Hlawatsch, H. Rauhut, G. Taubšck

Multichannel-compressive estimation of doubly selective channels in MIMO-OFDM systems: Exploiting and enhancing joint sparsity.

Proc. IEEE ICASSP 2010, Dallas, 2010.



P. Boufounos, G. Kutyniok, H. Rauhut

Average case analysis of sparse recovery from combined fusion frame measurements.

Proc. CISS 2010, Princeton, 2010. PDF



Y. Eldar, H. Rauhut

Average case analysis of multichannel basis pursuit.

Proc. SampTA09, Marseille, France, 2009. PDF



H. Rauhut

Circulant and Toeplitz matrices in compressed sensing.

Proc. SPARS'09, Saint-Malo, France, 2009. PDF



H. Rauhut

Identification of sparse operators.

Oberwolfach Reports 36:2130-2133, 2007. PDF



H. Rauhut

Average case analysis of multichannel thresholding

Proc. ICASSP 07, Hawaii, 2007 PDF

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