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Dr. Philipp Grohs

Prof. Dr. Philipp Grohs

Address

Seminar for Applied Mathematics
ETH Zürich
Rämistrasse 101
8092 Zurich
Switzerland



Research Interests



Press


Funding


Book


  1. Harmonic and Applied Analysis - From Groups to Signals. (Joint work with S. Dahlke, F. DeMari and D. Labate).
    Springer (2015). [link]

Scientific Publications


  1. Smoothness properties of Lie group subdivision schemes. (Joint work with J. Wallner and E. Nava Yazdani).
    SIAM Journal on Multiscale Modeling and Simulation 6 (2007), 493-505.
    [MR] [doi] [preprint].
  2. Log-exponential analogues of univariate subdivision schemes in Lie groups and their smoothness properties. (Joint work with J. Wallner).
    In M. Neamtu and L. L. Schumaker, editors, Approximation Theory XII: San Antonio 2007, pages 181-190. Nashboro Press, 2008, ISBN 978-0-9728482-9-9.
    [MR] [preprint].
  3. Smoothness analysis of subdivision schemes on regular grids by proximity.
    SIAM Journal on Numerical Analysis 46 (2008), 2169-2182.
    [MR] [doi] [preprint].
  4. Smoothness equivalence properties of univariate subdivision schemes and their projection analogues.
    Numerische Mathematik 113/2 (2009), 163-180.
    [MR] [doi] [preprint] .
  5. Smoothness of interpolatory multivariate subdivision in Lie groups.
    IMA Journal of Numerical Analysis 29/3 (2009), 760-772.
    [MR] [doi] [preprint] .
  6. Interpolatory wavelets for manifold-valued data. (Joint work with J. Wallner).
    Applied and Computational Harmonic Analysis 27 (2009), 325-333.
    [MR] [doi] [preprint] .
  7. Laguerre minimal surfaces, isotropic geometry and linear elasticity. (Joint work with H. Pottmann and N. Mitra).
    Advances in Computational Mathematics 31/2 (2009), 391-419.
    [MR] [doi] [preprint].
  8. Approximation order of interpolatory nonlinear subdivision schemes. (Joint work with N. Dyn and J. Wallner).
    Journal of Computational and Applied Mathematics 223 (2010), 1697-1703.
    [MR] [doi] [preprint].
  9. A general proximity analysis of nonlinear subdivision schemes.
    SIAM Journal on Mathematical Analysis 42/2 (2010), 729-750.
    [MR] [doi] [preprint].
  10. Approximation order from stability of nonlinear subdivision schemes.
    Journal of Approximation Theory 162 (2010), 1085-1094.
    [MR] [doi] [preprint].
  11. Edge offset meshes in Laguerre geometry. (Joint work with H. Pottmann and B. Blaschitz).
    Advances in Computational Mathematics 33/1 (2010), 45-73.
    [MR] [doi] [preprint].
  12. Stability of manifold-valued subdivision schemes and multiscale transformations.
    Constructive Approximation 32/3 (2010), 569-596.
    [MR] [doi] [preprint].
  13. The continuous Shearlet Transform: Representation Formulae and Microlocal Analysis.
    Oberwolfach Report 7/4 (2010).
    [doi]
  14. Continuous shearlet tight frames.
    Journal of Fourier Analysis and Applications 17/3 (2011), 506-518.
    [doi] [arXiv] [preprint].
  15. Continuous Shearlet frames and Resolution of the Wavefront Set.
    Monatshefte für Mathematik 164/4 (2011), 393-426.
    [doi] [arXiv] [preprint].
  16. Interpolating composite systems.
    In M. Neamtu and L. L. Schumaker, editors, Approximation Theory XIII: San Antonio 2010, Springer Proceedings in Mathematics 13 (2012), 111-120.
    [doi] [preprint].
  17. Shearlets and Microlocal Analysis.
    In: Shearlets: Multiscale Analysis for Multivariate Data, Birkhäuser-Springer (2012).
    [doi] [book] [preprint].
  18. Ridgelet-type Frame Decompositions for Sobolev Spaces related to linear Transport.
    Journal of Fourier Analysis and Applications 18/2 (2012), 309-325.
    [doi] [preprint].
  19. Definability and stability of multiscale decompositions for manifold-valued data. (Joint work with J. Wallner).
    Journal of the Franklin Institute 349/5 (2012), 1648-1664.
    [doi] [arXiv] [preprint].
  20. Tree Approximation with anisotropic decompositions.
    Applied and Computational Harmonic Analysis 33 (2012), 44-57.
    [doi] [preprint].
  21. Tree Approximation and optimal Image Coding with Shearlets.
    Proceedings SampTA: Singapore 2011 (2012).
    [preprint].
  22. On the Structure of Anisotropic Frames.
    Oberwolfach Report 29 (2012).
    [doi]
  23. Ruled Laguerre minimal surfaces. (Joint work with H. Pottmann and M. Skopenkov).
    Mathematische Zeitschrift 272/1 (2012), 645-674.
    [doi] [arXiv] [preprint].
  24. Bandlimited Shearlet Frames with nice Duals.
    Journal of Computational and Applied Mathematics 243 (2013), 139-151.
    [doi] [preprint].
  25. Refinable functions for dilation families.
    Advances in Computational Mathematics 38/3 (2013), 531-561.
    [doi] [arXiv] [preprint].
  26. Intrinsic Localization of Anisotropic Frames.
    Applied and Computational Harmonic Analysis 35/2 (2013), 264-283.
    [doi] [preprint].
  27. Finite Elements of Arbitrary Order and Quasiinterpolation for Riemannian Data.
    IMA Journal of Numerical Analysis 33/3 (2013), 849-874.
    [doi] [preprint].
  28. Geometric Multiscale Decompositions of Dynamic Low-Rank Matrices.
    Computer Aided Geometric Design 30 (2013), 805-826.
    [doi] [preprint].
  29. Parabolic Molecules. (Joint work with G. Kutyniok).
    Foundations of Computational Mathematics 14/2 (2014), 299-337.
    [doi] [preprint].
  30. Parabolic Molecules: Curvelets, Shearlets, and Beyond. (Joint work with S. Keiper, G. Kutyniok, M. Schaefer).
    In Approximation Theory XIV: San Antonio 2013, Springer Proceedings in Mathematics (2014), to appear.
    [preprint].
  31. $\alpha$-Molecules: Curvelets, Shearlets, Ridgelets, and Beyond. (Joint work with S. Keiper, G. Kutyniok, M. Schaefer).
    In Wavelets and Sparsity XV (San Diego, CA, 2013), SPIE Proc. 8858, SPIE, Bellingham, WA, (2014), to appear.
    [preprint].
  32. Wolfowitz's Theorem and Convergence of Consensus Algorithms in Hadamard Spaces.
    Proceedings of the American Mathematical Society (2014), to appear.
    [preprint].
  33. Hyperbolic Cross Approximation for the Spatially Homogenous Boltzmann Equation. (Joint work with E. Fonn and R. Hiptmair).
    IMA Journal of Numerical Analysis (2014), to appear.
    [doi] [preprint].
  34. Intrinsic Localization of Anisotropic Frames II: $\alpha$-molecules (Joint work with S. Vigogna).
    Journal of Fourier Analysis and Applications (2014), to appear.
    [doi] [preprint].
  35. Cartoon Approximation with $\alpha$-Curvelets (Joint work with S. Keiper, G. Kutyniok and M. Schaefer).
    Journal of Fourier Analysis and Applications (2014), to appear.
    [preprint].
  36. Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements. (Joint work with H. Hardering and O. Sander).
    Foundations of Computational Mathematics (2014), to appear.
    [doi] [preprint].
  37. FFRT-A Fast Finite Ridgelet Transform for Radiative Transport (Joint work with S. Etter and A. Obermeier).
    SIAM Journal on Multiscale Modeling and Simulation (2014), to appear.
    [preprint] [MATLAB codes].
  38. $\varepsilon$-Subgradient Algorithms for Locally Lipschitz Functions on Riemannian Manifolds (Joint work with S. Hosseini).
    Advances in Computational Mathematics (2015), to appear.
    [preprint].
  39. Optimal Adaptive Ridgelet Schemes for Linear Transport Equations (Joint work with A. Obermeier).
    Applied and Computational Harmonic Analysis (2015), to appear.
    [preprint].
  40. Ridgelet Methods for Linear Transport Equations (Joint work with A. Obermeier).
    In Curves and Surfaces: Paris 2014, Springer Proceedings in Mathematics (2015), to appear.
    [preprint]
  41. Nonsmooth Trust Region Algorithms for Locally Lipschitz Functions on Riemannian Manifolds (Joint work with S. Hosseini).
    IMA Journal of Numerical Analysis (2015), to appear.
    [preprint].
  42. $\alpha$-Molecules (Joint work with S. Keiper, G. Kutyniok and M. Schaefer).
    Applied and Computational Harmonic Analysis (2015), to appear.
    [preprint].
  43. Total Variation Regularization by Iteratively Reweighted Least Squares on Hadamard Spaces and the Sphere (Joint work with M. Sprecher).
    IMA Journal on Information and Inference (2015), to appear.
    [preprint]
  44. Deep convolutional neural networks on cartoon functions (Joint work with T. Wiatowski, and H. Bölcskei).
    Proc. of IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain, (2016), to appear.
    [preprint]
  45. Discrete Deep Feature Extraction: A Theory and New Architectures (Joint work with T. Wiatowski, M. Tschannen, A. Stanic and H. Boelcskei).
    Journal of Machine Learning Research (Proc. ICML 2016) (2016), to appear.
    [preprint]
  46. A Shearlet-Based Fast Thresholded Landweber Algorithm for Deconvolution (Joint work with Z. Kereta and U. Wiesmann).
    International Journal of Wavelets, Multiresolution and Information Processing (2016), to appear.
    [preprint].
  47. Scattered Manifold-Valued Data Approximation (Joint work with M. Sprecher and T. P.-Y. Yu).
    Numerische Mathematik (2016), accepted subject to revision.
    [preprint].
  48. On the maxima of cardinal refinable functions with positive symbol.
    Geometry preprint 2009/03, TU Graz, August 2009.
    [preprint].
  49. Sparse Twisted Tensor Frame Discretizations of Parametric Transport Equations. (Joint work with Ch. Schwab).
    SAM Report 2011-41, ETH Zurich, May 2011.
    [preprint].
  50. Projection-based Quasiinterpolation in Manifolds. (Joint work with M. Sprecher).
    SAM Report 2013-23, ETH Zurich, July 2013.
    [preprint] [MATLAB codes].
  51. Polar Spectral Scheme for the Spatially Homogenous Boltzmann Equation (Joint work with E. Fonn and R. Hiptmair).
    SAM Report 2014-13, ETH Zurich, April 2014.
    [preprint].
  52. Continuous Parabolic Molecules (Joint work with Z. Kereta).
    SAM Report 2015-17, ETH Zurich, July 2015.
    [preprint]
  53. Anisotropic Multiscale Systems on Bounded Domains (Joint work with G. Kutyniok, J. Ma and P. Petersen).
    SAM Report 2015-30, ETH Zurich, September 2015.
    [preprint]
  54. Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in 2D (Joint work with R. Hiptmair and S. Pintarelli).
    SAM Report 2015-38, ETH Zurich, November 2015.
    [preprint]
  55. On the Approximation of Functions with Line Singularities by Ridgelets (Joint work with A. Obermeier).
    SAM Report 2016-04, ETH Zurich, January 2016.
    [preprint]
  56. Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames (Joint work with R. Al-Aifari, I. Daubechies and G. Thakur).
    SAM Report 2016-08, ETH Zurich, January 2016.
    [preprint]
  57. Phase Retrieval in the general Setting of Continuous Banach Frames (Joint work with R. Al-Aifari).
    SAM Report 2016-21, ETH Zurich, April 2016.
    [preprint]

Theses


  1. Approximation Theory in Manifolds.
    Habilitation Thesis, TU Graz, 2010.
    [full thesis] [introduction].
  2. Smoothness Analysis of nonlinear Subdivison Schemes on regular grids.
    Phd Thesis, TU-Wien, 2007.
    [pdf].
  3. Asymptotik von Goppa Codes (in German).
    Diploma Thesis, TU-Wien, 2006.
    [pdf].
  4. Beweis der Bieberbachschen Vermutung (in German).
    Semester Thesis, TU-Wien, 2005.
    [pdf].