Computational Harmonic Analysis, Mathematical Data and Image Analysis

The main theme of my mathematical research is Computational Harmonic Analysis with a special focus on Mathematical Data Analysis and Image Processing. 

The research group is integrated into the NuHAG. 

I am Vice-Director of Studies at the Faculty of Mathematics and I am co-organizer of the bi-annual conference on Applied Harmonic Analysis in Strobl/Austria.

Preprints

  • M. Ehler, K. Gröchenig: t-design curves and mobile sampling on the sphere, arXiv 2023.
  • M. Ehler, K. Gröchenig: Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities, arXiv 2022.
  • A. Breger, C. Karner, M. Ehler: visClust: A visual clustering algorithm based on orthogonal projections, arXiv, 2022.

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, (Springer) Constr. Approx., (2023).
  • M. Ehler, M. Gräf, S. Neumayer, G. Steidl: Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization (Springer) Found. Comput. Math. 2021 
  • 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 
  • 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) IEEE Trans. Inform. Theory, vol. 61 (2015), no. 7, 1-13. 
  • M. Ehler, M. Fornasier, J. Sigl: Quasi-linear compressed sensing (arXiv) 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) IEEE Trans. Pattern Anal. Mach. Intell. vol. 35 (2013), no. 5, 1274-1280.
  • M. Ehler and B. Han: Wavelet bi-frames with few generators from multivariate refinable functions (sciencedirect) Appl. Comput. Harmon. Anal., vol. 25 (2008), no. 3, 407-414.