Assoc. Prof. Martin Ehler Head of: Vienna Research Group for Young Investigators

University of Vienna Faculty of Mathematics Oskar-Morgenstern-Platz 1 A-1090 Vienna Room: 10.128 Phone: +43 1 4277 50729 martin.ehler'at'univie.ac.at

Office hours: Thursday, 2:30-4:00 pm, via my zoom office

Computational harmonic analysis of high-dimensional biomedical data (CHARMED)

WWTF Program Mathematics and ... ,
in collaboration with the Vienna Reading Center (VRC) at the Department of Ophthalmology and Optometry of the Medical University of Vienna and with the Acoustics Research Institute (ARI) of the Austrian Academy of Sciences.

The research group is integrated into the NuHAG.

Selected publications:

• 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 )
  accepted in Constr. Approx. 2021
• M. Ehler, M. Gräf, S. Neumayer, G. Steidl: Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization, (pdf)
  Found. Comput. Math. 2021
• 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.
• 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, (Epub)
  Eye, Springer Nature, 2017
• B. G. Bodmann, M. Ehler, M. Gräf: From low to high-dimensional moments without magic, (arXiv:1601.07401)
  J. Theor. Probab., (2017)
• M. Ehler, J. Dobrosotskaya, et al.: Modeling photo-bleaching kinetics to create high resolution maps of rod rhodopsin in the human retina, (e-paper)
  PLoS ONE, vol. 10 (2015), no. 7, e0131881.
• 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.
• 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.
• W. Czaja, M. Ehler: Schroedinger Eigenmaps for the analysis of bio-medical data, (arXiv:1102.4086)
  IEEE Trans. Pattern Anal. Mach. Intell. vol. 35 (2013), no. 5, 1274-1280.
• 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.
• M. Ehler, K. Okoudjou: Minimization of the p-th probabilistic frame potential, (pdf)
  J. Statist. Plann. Inference, vol. 142 (2012), no. 3, 645-659.
• M. Ehler, F. Filbir, H. Mhaskar: Locally learning biomedical data using diffusion frames,
  J. Comput. Biol. vol. 19 (2012), no. 11, 1251-64.
• M. Ehler and B. Han: Wavelet bi-frames with few generators from multivariate refinable functions, (pdf)
  Appl. Comput. Harmon. Anal., vol. 25 (2008), no. 3, 407-414.