Institute for
Numerical Simulation

Research Group
H. 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:	rauhuthcm.uni-bonn.de

News

• My daughter Antonella was born on April 22, 2012.
• Invited Speaker at Summer School on Applied Analysis, September 24 - 28, Chemnitz University of Technology.
• Special Issue on Sparse Approximate Solution of Linear Systems, Linear Algebra and Its Applications, Guest Editors: Gitta Kutyniok, Holger Rauhut, Allan Pinkus, Vladimir Temlyakov.
• CoSeRa2012, 1st International Workshop on Compressed Sensing Applied to Radar, Bonn, May 14 - 16, 2012, Organizers: Joachim Ender, Holger Rauhut, Ludger Prünte, Matthias Weiss, Jens Fiege, Laura Anitori.
• Best Paper Award 2010 of the Journal of Complexity for the paper The Gelfand widths of lp-balls for 0 < p <=1 by Simon Foucart, Alain Pajor, Holger Rauhut and Tino Ullrich.
• Plenary speaker at International Conference on Multivariate Approximation, September 24-27, 2011, Hagen.
• Workshop on Random Matrices, Bonn, May 29 - June 1, 2012, Organizers: Patrik Ferrari, Holger Rauhut, Benjamin Schlein.
• Random Matrix Day, Bonn, February 14, 2011.
• Oberwolfach Workshop Applied Harmonic Analysis and Sparse Approximation, June 10 - 16, 2012, Organizers: Ingrid Daubechies, Gitta Kutyniok, Holger Rauhut, Thomas Strohmer.
• The ERC Starting Grant "Sparse and Low Rank Recovery" has been accepted by the ERC, Press Release.
• I will be visiting ETH Zurich, Seminar for Applied Mathematics from mid February to mid April 2011.
• Minisymposium on Compressed Sensing and Sparse Approximation Algorithms at ILAS 2011, Braunschweig, August 22 - 26, 2011, Organizers: Gitta Kutyniok and Holger Rauhut.
• Invited Speaker at conference From Abstract to Computational Harmonic Analysis, Strobl, June 13 - 19, 2011.
• Organization of a special session on sparse approximation at SampTA11, Singapore, May 2 - 6, 2011.
• Schülerwoche Mathematik 2010.
• Radio interview on compressed sensing (in german).
• Workshop Sparse and Low Rank Approximation, Banff International Research Station, March 6 - 11, 2011. Organizers: Gitta Kutyniok, Holger Rauhut, Joel Tropp, Özgür Yilmaz.
• Invited Speaker at Conference New Trends in Harmonic and Complex Analysis, June 28 - July 2, 2010, Jacobs University Bremen.
• Invited Speaker at Workshop Probability and Geometry in High Dimensions, May 17 - 21, 2010, Marne-la-Vallée.
• Associate Editor for Acta Applicandae Mathematicae.
• Workshop Sparsity and Computation, Hausdorff Center for Mathematics Bonn, June 7-11, 2010. Organizers: Ron DeVore, Massimo Fornasier, Holger Rauhut; Pictures and Slides.
• Vortrag "Signalrekonstruktion trotz unvollständiger Daten" beim Aktionstag Mathematik, Mathematik-Zentrum Bonn, Samstag, 26. September 2009.
• Short Course on "Compressive sensing and structured random matrices" at Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery", Linz, August 31-September 4, 2009, Lecture Notes (Version of April 4, 2011), Slides.

CV

Education

• 1995 Abitur at Alexander-von-Humboldt-Gymnasium Konstanz
• 1996 - 2001 Mathematical Studies at the Technical University Munich
• 2000 One semester at the National University of Singapore
• 2002 - 2004 Doctorate studies at the Graduate Program Applied Algorithmic Mathematics at the Technical University Munich (doctorate degree: December 2004)
• June 2008 Habilitation, University of Vienna

Academic Positions

• January - March 2005 PostDoc in the European research network HARP at the Faculty of Mathematics, University of Wroclaw, Poland
• April 2005 - February 2006 PostDoc in the European research network HASSIP at Numerical Harmonic Analysis Group (NuHAG), University of Vienna
• March 2006 - February 2008 Individual Marie Curie Fellowship at NuHAG
• Since March 2008 W2-Professor (Bonn Junior Fellow) at Hausdorff Center for Mathematics, University of Bonn.

Teaching

• WS 2011/2012:
  Lecture Advanced Topics in Scientific Computing - Applied Harmonic Analysis, module V5E1, Course Announcement
  
• WS 2011/2012:
  Seminar Graduate Seminar on Probability Theorey - Random Matrices, module S4F1, Course Announcement
  Joint Seminar with Prof. Dr. Benjamin Schlein
  
• SS 2011:
  Lecture Selected Topics in Scientific Computing - Compressed Sensing, module V5E2
  
• SS 2011:
  Post-graduate Seminar Graduate Seminar on Numerical Analysis - Applied Harmonic Analysis, module S5E1
  
• WS 2010/2011:
  Lecture Selected Topics in Scientific Computing - Mathematical Learning Theory, module V5E2
  
• WS 2010/2011:
  Lecture Selected Topics in Scientific Computing - Wavelets, module V5E2
  
• WS 2010/2011:
  Post-graduate Seminar Graduate Seminar on Scientific Computing - Applied Harmonic Analysis, module S4E1
  
• SS 2010:
  Lecture Selected Topics in Scientific Computing - Regularization of Inverse Problems, module V5E2
  
• SS 2010:
  Seminar Algorithmen der modernen Approximationstheorie, module S1G1
  
• SS 2010:
  Oberseminar Scientific Computing
  
• WS 2009/2010:
  Lecture Advanced Topics in Scientific Computing - Convex Optimization, module V5E1
  
• WS 2009/2010:
  Post-graduate Seminar Graduate Seminar on Scientific Computing, module S4E1
  
• SS 2009:
  Lecture Advanced Topics in Scientific Computing - Approximation Theory, module V5E1
  
• SS 2009:
  Numerische lineare Algebra, module S1G1
  Seminar with Prof. Dr. Alexey Chernov.
• SS 2009:
  Post-graduate Seminar Angewandte Harmonische Analysis
  
• WS 2008/2009:
  Lecture Selected Topics in Scientific Computing - Compressed Sensing, module V5E2
  
• WS 2008/2009:
  Post-graduate Seminar Graduate Seminar on Scientific Computing - Wavelets, module S4E1
  
• SS 2008:
  Lecture Advanced Topics in Scientific Computing - Zeit-Frequenz-Analyse , module V5E4
  

Publications

Preprints:

[1]	M. Hügel, H. Rauhut, and T. Strohmer. Remote sensing via l1-minimization. Preprint, 2012. [ bib | .pdf 1 ]
[2]	U. Ayaz and H. Rauhut. Nonuniform sparse recovery with subgaussian matrices. Preprint, 2011. [ bib | .pdf 1 ]
[3]	G. Pfander, H. Rauhut, and J. Tropp. The restricted isometry property for time-frequency structured random matrices. Preprint, 2011. [ bib | .pdf 1 ]

Journal Papers:

[1]	H. Rauhut and R. Ward. Sparse Legendre expansions via l1-minimization. J. Approx. Theory, 164(5):517-533, 2012. [ bib | DOI | .pdf 1 ]
[2]	H. Rauhut, J. Romberg, and J. Tropp. Restricted isometries for partial random circulant matrices. Appl. Comput. Harmonic Anal., 32(2):242-254, 2012. [ bib | DOI | .pdf 1 ]
[3]	P. Boufounos, G. Kutyniok, and H. Rauhut. Sparse recovery from combined fusion frame measurements. IEEE Trans. Inform. Theory, 57(6):3864-3876, 2011. [ bib | DOI | .pdf 1 ]
[4]	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. [ bib | DOI | .pdf 1 ]
[5]	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. [ bib | DOI | .pdf 1 ]
[6]	G. E. Pfander and H. Rauhut. Sparsity in time-frequency representations. J. Fourier Anal. Appl., 16(2):233-260, 2010. [ bib | DOI | .pdf 1 ]
[7]	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. [ bib | DOI | .pdf 1 ]
[8]	Y. Eldar and H. Rauhut. Average case analysis of multichannel sparse recovery using convex relaxation. IEEE Trans. Inform. Theory, 56(1):505-519, 2010. [ bib | DOI | .pdf 1 ]
[9]	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. [ bib | DOI | .pdf 1 ]
[10]	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. [ bib | DOI | .pdf 1 ]
[11]	M. Fornasier and H. Rauhut. Recovery algorithms for vector valued data with joint sparsity constraints. SIAM J. Numer. Anal., 46(2):577-613, 2008. [ bib | DOI | .pdf 1 ]
[12]	M. Fornasier and H. Rauhut. Iterative thresholding algorithms. Appl. Comput. Harmon. Anal., 25(2):187-208, 2008. [ bib | DOI | .pdf 1 ]
[13]	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. [ bib | DOI | .pdf 1 ]
[14]	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. [ bib | DOI | .pdf 1 ]
[15]	G. E. Pfander, H. Rauhut, and J. Tanner. Identification of matrices having a sparse representation. IEEE Trans. Signal Process., 56(11):5376-5388, 2008. [ bib | DOI | .pdf 1 ]
[16]	H. Rauhut. Stability results for random sampling of sparse trigonometric polynomials. IEEE Trans. Information Theory, 54(12):5661-5670, 2008. [ bib | DOI | .pdf 1 ]
[17]	H. Rauhut. On the impossibility of uniform sparse reconstruction using greedy methods. Sampl. Theory Signal Image Process., 7(2):197-215, 2008. [ bib | .pdf 1 ]
[18]	H. Rauhut, K. Schnass, and P. Vandergheynst. Compressed sensing and redundant dictionaries. IEEE Trans. Inform. Theory, 54(5):2210-2219, 2008. [ bib | DOI | .pdf 1 ]
[19]	R. Lasser, J. Obermaier, and H. Rauhut. Generalized hypergroups and orthogonal polynomials. J. Aust. Math. Soc., 82(3):369-393, 2007. [ bib | .pdf 1 ]
[20]	H. Rauhut. Coorbit Space Theory for Quasi-Banach Spaces. Studia Math., 180(3):237-253, 2007. [ bib | .pdf 1 ]
[21]	H. Rauhut. Wiener amalgam spaces with respect to quasi-Banach spaces. Colloq. Math., 109(2):345-362, 2007. [ bib | .pdf 1 ]
[22]	H. Rauhut. Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon. Anal., 22(1):16-42, 2007. [ bib | DOI | .pdf 1 ]
[23]	H. Rauhut. Radial Time-Frequency Analysis and Embeddings of Radial Modulation Spaces. Sampl. Theory Signal Image Process., 5(2):201-224, 2006. [ bib | .pdf 1 ]
[24]	M. Fornasier and H. Rauhut. Continuous Frames, Function Spaces, and the Discretization Problem. J. Fourier Anal. Appl., 11(3):245-287, 2005. [ bib | DOI | .pdf 1 ]
[25]	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. [ bib | DOI | .pdf 1 ]
[26]	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. [ bib | DOI | .pdf 1 ]
[27]	H. Rauhut. Best time localized trigonometric polynomials and wavelets. Adv. Comput. Math., 22(1):1-20, 2005. [ bib | DOI | .ps.gz 1 ]
[28]	H. Rauhut and M. Rösler. Radial multiresolution in dimension three. Constr. Approx., 22(2):167-188, 2005. [ bib | DOI | .pdf 1 ]
[29]	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. [ bib | DOI | .ps.gz 1 ]

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. [ bib | DOI | .pdf 1 ]

[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. [ bib | http | .pdf 1 ]

Proceeding Papers:

[1]	A. Cohen, R. DeVore, S. Foucart, and H. Rauhut. Recovery of functions of many variables via compressive sensing. In Proc. SampTA 2011, Singapore, 2011. [ bib | .pdf 1 ]
[2]	H. Rauhut and R. Ward. Sparse recovery for spherical harmonic expansions. In Proc. SampTA 2011, Singapore, 2011. [ bib | .pdf 1 ]
[3]	H. Rauhut. Sparse and low rank recovery. In Oberwolfach Reports, 2011. [ bib | .pdf 1 ]
[4]	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. [ bib ]
[5]	P. Boufounos, G. Kutyniok, and H. Rauhut. Average case analysis of sparse recovery from combined fusion frame measurements. In Proc. CISS 2010, Princeton, 2010. [ bib | .pdf 1 ]
[6]	H. Rauhut. Compressive sensing, structured random matrices and recovery of functions in high dimensions. In Oberwolfach Reports, volume 7, pages 1990-1993, 2010. [ bib | .pdf 1 ]
[7]	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'. [ bib | .pdf 1 ]
[8]	P. Boufounos, G. Kutyniok, and H. Rauhut. Compressed sensing for fusion frames. In Proc. SPIE Wavelets XIII, 2009. [ bib | .pdf 1 ]
[9]	Y. Eldar and H. Rauhut. Average case analysis of multichannel basis pursuit. In Proc. SampTA09, Marseille, France, 2009. [ bib | .pdf 1 ]
[10]	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. [ bib | .pdf 1 ]
[11]	H. Rauhut. Identification of sparse operators. In Oberwolfach Reports, volume 4, pages 2130-2133, 2007. [ bib | .pdf 1 ]

Thesis:

[1]	H. Rauhut. Sparse Recovery. 2007. Habilitation Thesis. University of Vienna. (Date of Defense: June 4, 2008). [ bib | .pdf 1 ]
[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). [ bib | http ]
[3]	H. Rauhut. An uncertainty principle for periodic functions. 2001. Diploma Thesis. Technical University of Munich. [ bib | .pdf 1 ]

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. [ bib | .pdf 1 ]