Project related publications

    Preprints (available upon request)
  1. M. Ehler, M. Gräf, S. Neumayer, G. Steidl: Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization, (arXiv:1910.06124 )
  2. J. Dick, M. Ehler, M. Gräf, C. Krattenthaler: Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold, (arXiv:1909.12334 )
  3. M. Ehler, G. Gigante, T. Peter: On the existence of asymptotically optimal cubature points, (arXiv:1810.01106)

  4. Peer-reviewed publications
  5. A. Breger, J. I. Orlando, P. Harar, M. Doerfler, S. Klimscha, C. Grechenig, B. S. Gerendas, U. Schmidt-Erfurth, and M. Ehler: On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems, (arXiv:1901.07598)
    accepted in Journal of Mathematical Imaging and Vision (JMIV) 2019
  6. M. Ehler, S. Kunis, T. Peter, C. Richter: A Randomized Multivariate Matrix Pencil Method for Superresolution Microscopy, (arXiv:1805.02485)
    Electronic Transactions on Numerical Analysis vol. 51, (2019), 63-74.
  7. M. Ehler, M. Gräf, C. J. Oates: Optimal Monte Carlo integration on closed manifolds, (arXiv:1707.04723)
    Statistics and Computing vol 29 (2019), no. 6, 1203-1214.
  8. M. Ehler, M. Gräf: Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians, (arXiv:1411.5865)
    Constr. Approx., vol. 49 (2018), no. 1, 29-58.
  9. A. Breger, M. Ehler, M. Gräf: Points on manifolds with asymptotically optimal covering radius, (arXiv:1607.06899)
    Journal of Complexity 2018.
  10. M. Ehler, F. Filbir: Metric entropy, n-widths, and sampling of functions on manifolds, (arXiv:1311.1393)
    J. Approx. Theory, vol. 225 (2018), 41-57.
  11. M. Ehler, M. Gräf: Numerically optimizing weights for Monte Carlo integration on smooth compact manifolds, (arXiv:1707.04723)
    19th International Symposium on Symbolic and Numeric Algorithms for Scientifc Computing
  12. B. G. Bodmann, M. Ehler, M. Gräf: From low to high-dimensional moments without magic, (arXiv:1601.07401)
    J. Theor. Probab., (2017)
  13. A. Breger, M. Ehler, M. Gräf, T. Peter: Cubatures on Grassmannians: moments, dimension reduction, and related topics, (arXiv:1705.02978)
    Compressed Sensing and its Applications: MATHEON Workshop 2015 (Applied and Numerical Harmonic Analysis), 2017.
  14. A. Breger, M. Ehler: Sampling in Grassmannians,
    SampTA 2017, Sampling Theorie and Applications, Tallinn.
  15. A. Breger, M. Ehler, H. Bogunovic, S.M. Waldstein, A. Philip, U. Schmidt-Erfurth, B.S. Gerendas: Supervised learning and dimension reduction techniques for quantification of retinal fluid in optical coherence tomography images,
    Eye, Springer Nature 2017.
  16. M. Velimirovic, S. Wagner, M. Gräf, M. Ehler, F. A. Monikh, F. von der Kammer, T. Hofmann: TiO2 nanoparticles in sunscreens using asymmetric flow field-flow fractionation hyphenated to ICPMS: from mass based to number based particle size distribution.
    NanoImpact Conference, Monte Verita, Switzerland, 2017, Poster.
  17. M. Velimirovic, S. Wagner, M. Gräf, M. Ehler, F. A. Monikh, F. von der Kammer, T. Hofmann: TiO2 nanoparticles in sunscreen lotion: asymmetric flow field-flow fractionation hyphenated to ICPMS for their characterization.
    253rd ACS National Meeting and Exposition, San Francisco, USA, 2017, Presentation.
  18. A. Breger, H. Bogunovic, B.S. Gerendas, U. Schmidt-Erfurth, M. Ehler: An efficient learning pipeline for quantification of retinal fluid in spectral-domain optical coherence tomography images.
    2nd IMA Conference on the Mathematical Challenges of Big Data, London.
  19. A. Breger, M. Ehler, M. Gräf: Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians, (arXiv:1605.09165)
    Frames and Other Bases in Abstract and Function Spaces, Applied and Numerical Harmonic Analysis series (ANHA), Birkhauser/Springer (2017)
  20. F. Bachoc, M. Ehler, M. Gräf: Optimal configurations of lines and a statistical application, (arXiv:1503.00444)
    Advances in Computational Mathematics, vol. 43, no. 1, (2017), 113-126.
  21. M. Ehler, M. Gräf, F. Király: Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices,
    Waves, Wavelets and Fractals - Advanced Analysis, vol. 1, no. 1 (2015).
  22. J. Cahill, P. G. Casazza, M. Ehler, S. Li: Tight and random nonorthogonal fusion frames,
    Trends in Harmonic Analysis and Its Applications, Contemporary Mathematics, vol. 650 (2015), 23-36.
  23. M. Ehler, J. Dobrosotskaya, et al.: Modeling photo-bleaching kinetics to create high resolution maps of rod rhodopsin in the human retina,
    PLoS ONE, vol. 10 (2015), no. 7, e0131881.
  24. M. Ehler: Preconditioning filter bank decompositions using structured normalized tight frames, (arXiv:1305.0716)
    J. Appl. Math. (2015)
  25. C. Bachoc, M. Ehler: Signal reconstruction from the magnitude of subspace components, (arXiv:1209.5986)
    IEEE Trans. Inform. Theory, vol. 61 (2015), no. 7, 1-13.
  26. M. Ehler, F. Filbir: Wavelet frames to optimally learn functions on diffusion measure spaces,
    Current Trends in Analysis and its Applications, Mityushev, Vladimir V., Ruzhansky, Michael (Eds.), 9th International ISAAC Congress, Birkhäuser Mathematik, 2015, 715-720.
  27. M. Ehler, F. Filbir: ε-coverings of Hölder-Zygmund type spaces on data-defined manifolds,
    Abstract and Applied Analysis, Special Issue on Scaling, Self-Similarity, and Systems of Fractional Order, Article ID 402918 (2014).
  28. M. Ehler, M. Fornasier, J. Sigl: Quasi-linear compressed sensing, (arXiv:1311.1642v1)
    SIAM Multiscale Modeling and Simulation, vol. 12 (2014), no. 2, 725-754.
  29. J. J. Benedetto, W. Czaja, M. Ehler: Wavelet Packets for time-frequency analysis of multi-spectral images,
    International Journal on Geomathematics (GEM), vol. 4 (2013), 137-154.
  30. M. Ehler: Modifications of iterative schemes used for curvature correction in noninvasive noncontact biomedical imaging,
    J. Biomed. Optics, vol. 18 (2013), no. 10, 100503.