Research Group of Prof. Dr. H. Rauhut
Institute for Numerical Simulation
maximize

Prof. Dr. Holger Rauhut

Prof. Dr. Holger Rauhut
Address: Hausdorff Center for Mathematics
Endenicher Allee 60
53115 Bonn
Germany
Office: LWK 4.028
Phone: +49 228 73 62245
E-Mail: rauhut.hcm.uni-bonn.de

News

CV

Education

Academic Positions

Teaching

Publications

Preprints:

[1] N. Ailon and H. Rauhut. Fast and RIP-optimal transforms. Preprint, 2013.
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[2] M. Kabanava and H. Rauhut. Analysis l1-recovery with frames and Gaussian measurements. Preprint, 2013.
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[3] U. Ayaz and H. Rauhut. Sparse recovery of fusion frame structured signals. (This is an early draft and will soon be updated).
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[4] U. Ayaz and H. Rauhut. The restricted isometry property for fusion frame structured sparse signals. (This is an early draft and will soon be updated).
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Journal Papers:

[1] U. Ayaz and H. Rauhut. Nonuniform sparse recovery with subgaussian matrices. ETNA, to appear.
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[2] F. Krahmer, S. Mendelson, and H. Rauhut. Suprema of chaos processes and the restricted isometry property. Comm. Pure Appl. Math., to appear.
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[3] G. Pfander, H. Rauhut, and J. Tropp. The restricted isometry property for time-frequency structured random matrices. Prob. Theory Rel. Fields, to appear.
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[4] M. Hügel, H. Rauhut, and T. Strohmer. Remote sensing via l1-minimization. Found. Comput. Math., to appear.
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[5] H. Rauhut and R. Ward. Sparse Legendre expansions via l1-minimization. J. Approx. Theory, 164(5):517-533, 2012.
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[6] H. Rauhut, J. Romberg, and J. Tropp. Restricted isometries for partial random circulant matrices. Appl. Comput. Harmonic Anal., 32(2):242-254, 2012.
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[7] P. Boufounos, G. Kutyniok, and H. Rauhut. Sparse recovery from combined fusion frame measurements. IEEE Trans. Inform. Theory, 57(6):3864-3876, 2011.
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[8] T. Ullrich and H. Rauhut. Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type. J. Funct. Anal., 260(11):3299-3362, 2011.
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[9] M. Fornasier, H. Rauhut, and R. Ward. Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM J. Optimization, 21(4):1614-1640, 2011.
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[10] G. E. Pfander and H. Rauhut. Sparsity in time-frequency representations. J. Fourier Anal. Appl., 16(2):233-260, 2010.
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[11] G. Tauböck, D. Eiwen, F. Hlawatsch, and H. Rauhut. 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.
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[12] Y. Eldar and H. Rauhut. Average case analysis of multichannel sparse recovery using convex relaxation. IEEE Trans. Inform. Theory, 56(1):505-519, 2010.
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[13] S. Foucart, A. Pajor, H. Rauhut, and 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.
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[14] S. Dahlke, M. Fornasier, H. Rauhut, G. Steidl, and G. Teschke. Generalized Coorbit Theory, Banach Frames, and the Relation to alpha-Modulation Spaces. Proc. London Math. Soc. (3), 96:464-506, 2008.
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[15] M. Fornasier and H. Rauhut. Recovery algorithms for vector valued data with joint sparsity constraints. SIAM J. Numer. Anal., 46(2):577-613, 2008.
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[16] M. Fornasier and H. Rauhut. Iterative thresholding algorithms. Appl. Comput. Harmon. Anal., 25(2):187-208, 2008.
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[17] R. Gribonval, H. Rauhut, K. Schnass, and 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.
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[18] S. Kunis and H. Rauhut. Random sampling of sparse trigonometric polynomials II - orthogonal matching pursuit versus basis pursuit. Found. Comput. Math., 8(6):737-763, 2008.
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[19] G. E. Pfander, H. Rauhut, and J. Tanner. Identification of matrices having a sparse representation. IEEE Trans. Signal Process., 56(11):5376-5388, 2008.
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[20] H. Rauhut. Stability results for random sampling of sparse trigonometric polynomials. IEEE Trans. Information Theory, 54(12):5661-5670, 2008.
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[21] H. Rauhut. On the impossibility of uniform sparse reconstruction using greedy methods. Sampl. Theory Signal Image Process., 7(2):197-215, 2008.
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[22] H. Rauhut, K. Schnass, and P. Vandergheynst. Compressed sensing and redundant dictionaries. IEEE Trans. Inform. Theory, 54(5):2210-2219, 2008.
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[23] R. Lasser, J. Obermaier, and H. Rauhut. Generalized hypergroups and orthogonal polynomials. J. Aust. Math. Soc., 82(3):369-393, 2007.
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[24] H. Rauhut. Coorbit Space Theory for Quasi-Banach Spaces. Studia Math., 180(3):237-253, 2007.
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[25] H. Rauhut. Wiener amalgam spaces with respect to quasi-Banach spaces. Colloq. Math., 109(2):345-362, 2007.
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[26] H. Rauhut. Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon. Anal., 22(1):16-42, 2007.
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[27] H. Rauhut. Radial Time-Frequency Analysis and Embeddings of Radial Modulation Spaces. Sampl. Theory Signal Image Process., 5(2):201-224, 2006.
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[28] M. Fornasier and H. Rauhut. Continuous Frames, Function Spaces, and the Discretization Problem. J. Fourier Anal. Appl., 11(3):245-287, 2005.
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[29] 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.
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[30] 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.
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[31] H. Rauhut. Best time localized trigonometric polynomials and wavelets. Adv. Comput. Math., 22(1):1-20, 2005.
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[32] H. Rauhut and M. Rösler. Radial multiresolution in dimension three. Constr. Approx., 22(2):167-188, 2005.
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[33] J. Prestin, E. Quak, H. Rauhut, and 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.
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Book Contributions:

[1] M. Fornasier and H. Rauhut. Compressive Sensing. In O. Scherzer, editor, Handbook of Mathematical Methods in Imaging, pages 187-228. Springer, 2011.
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[2] 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. Corrected Version (April 4, 2011): Noncommutative Khintchine inequality for Rademacher chaos (Theorem 6.22) corrected, Proof of Theorem 9.3 corrected. Proof of Lemma 8.2 corrected.
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Proceeding Papers:

[1] U. Ayaz and H. Rauhut. Nonuniform sparse recovery with fusion frames. 2013. submitted to Proc. SPARS'13.
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[2] H. Rauhut, R. Schneider, and Z. Stojanac. Low rank tensor tensor recovery via iterative hard thresholding. 2013. Proc. SampTA 2013.
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[3] M. Kabanava and H. Rauhut. Recovery of cosparse signals with Gaussian measurements. 2013. Proc. SampTA 2013.
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[4] U. Ayaz and H. Rauhut. Sparse recovery with fusion frames via RIP. 2013. Proc. SampTA 2013.
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[5] A. Cohen, R. DeVore, S. Foucart, and H. Rauhut. Recovery of functions of many variables via compressive sensing. In Proc. SampTA 2011, Singapore, 2011.
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[6] H. Rauhut and R. Ward. Sparse recovery for spherical harmonic expansions. In Proc. SampTA 2011, Singapore, 2011.
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[7] H. Rauhut. Sparse and low rank recovery. In Oberwolfach Reports, 2011.
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[8] G. Tauböck, F. Hlawatsch, D. Eiwen, H. Rauhut, and N. Czink. Multichannel-compressive estimation of doubly selective channels in MIMO-OFDM systems: Exploiting and enhancing joint sparsity. In Proc. IEEE ICASSP 2010, Dallas, 2010.
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[9] P. Boufounos, G. Kutyniok, and H. Rauhut. Average case analysis of sparse recovery from combined fusion frame measurements. In Proc. CISS 2010, Princeton, 2010.
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[10] H. Rauhut. Compressive sensing, structured random matrices and recovery of functions in high dimensions. In Oberwolfach Reports, volume 7, pages 1990-1993, 2010.
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[11] H. Rauhut. Circulant and Toeplitz matrices in compressed sensing. In Proc. SPARS'09, Saint-Malo, France, 2009. Note: Material mostly superseded by corresponding chapters in the book contribution 'Compressive Sensing and Structured Random Matrices'.
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[12] P. Boufounos, G. Kutyniok, and H. Rauhut. Compressed sensing for fusion frames. In Proc. SPIE Wavelets XIII, 2009.
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[13] Y. Eldar and H. Rauhut. Average case analysis of multichannel basis pursuit. In Proc. SampTA09, Marseille, France, 2009.
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[14] R. Gribonval, B. Mailhe, H. Rauhut, K. Schnass, and P. Vandergheynst. Average case analysis of multichannel thresholding. In Proc. IEEE Intl. Conf. Acoust. Speech Signal Process., 2007.
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[15] H. Rauhut. Identification of sparse operators. In Oberwolfach Reports, volume 4, pages 2130-2133, 2007.
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Thesis:

[1] H. Rauhut. Sparse Recovery. 2007. Habilitation Thesis. University of Vienna. (Date of Defense: June 4, 2008).
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[2] H. Rauhut. Time-Frequency and Wavelet Analysis of Functions with Symmetry Properties. Logos-Verlag, 2004. Doctoral Thesis. Technical University of Munich. (Date of Defense: December 16, 2004).
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[3] H. Rauhut. An uncertainty principle for periodic functions. 2001. Diploma Thesis. Technical University of Munich.
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Other Reports:

[1] K. Gröchenig, B. Pötscher, and H. Rauhut. Learning trigonometric polynomials from random samples and exponential inequalities for eigenvalues of random matrices, 2007.
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