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

We are part of the Applied Harmonic Analysis Cluster (AHA).

I am Vice-Dean for Teaching at the Faculty of Mathematics and I co-organize the bi-annual conference on Applied Harmonic Analysis in Strobl/Austria.

Preprints

• M. Ehler, K. Gröchenig: Quantitative constraints for stable sampling on the sphere, preprint, 2026.
• M. Ehler: Hybrid spherical designs, preprint, 2025.
• M. Ehler, K. Gröchenig, C. Karner: Geodesic cycles on the Sphere: t-designs and Marcinkiewicz-Zygmund Inequalities, preprint, 2025.

Publications of the last 5 years

• D. Haider, M. Ehler, P. Balazs: Injectivity of ReLU-layers: Perspectives from Frame Theory, accepted in SIAM Mathematical Foundations of Machine Learning, 2025.
• V. Lostanlen, X. Zhang, D. Haider, M. Lagrange, M. Ehler, P. Balazs: Residual hybrid filterbanks, IEEE Statistical Signal Processing Workshop (SSP), 2025.
• M. Dörfler, M. Ehler, K. Gröchenig, A. Klotz: Approximation of the short-time Fourier transform, 15th International Conference on Sampling Theory and Applications (SampTA), 2025.
• C. Karner, M. Ehler, P. R. López-Gómez: Asymptotically optimal t-design curves on the Grassmann manifold, 15th International Conference on Sampling Theory and Applications (SampTA), 2025.
• M. Ehler, K. Gröchenig, A. Klotz: Quantitative estimates: how well does the discrete Fourier transform approximate the Fourier transform on R, accepted in SIAM Rev. (Spotlight), 2025, preprint.
• H. Eckert, D. Haider, M. Ehler, P. Balazs: Invertibility of ReLU-layers: A Practical Approach, accepted in 16th International Conference on Neural Computation Theory and Applications (NCTA) 2024.
• D. Haider, F. Perfler, V. Lostanlen, M. Ehler, P. Balazs: Hold Me Tight: Stable Encoder-Decoder Design for Speech Enhancement, Interspeech 2024.
• D. Haider, V. Lostanlen, M. Ehler, P. Balazs: Instabilities in Convnets for Raw Audio, IEEE Signal Processing Letters, 31:1084-1088, 2024.
• A. Breger, C. Karner, M. Ehler: visClust: A visual clustering algorithm based on orthogonal projections, Pattern Recognition, 148, 2024.
• M. Ehler, K. Gröchenig: An abstract approach to Marcinkiewicz-Zygmund inequalities for approximation and quadrature in modulation spaces, Mathematics of Computation, 2023.
• M. Ehler, K. Gröchenig: t-design curves and mobile sampling on the sphere, Forum of Mathematics, Sigma, 11, 2023.
• V. Lostanlen, D. Haider, H. Han, M. Lagrange, P. Balazs, M. Ehler: Fitting auditory filterbanks with multiresolution neural networks, WASPAA, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2023.
• D. Haider, M. Ehler, P. Balazs: Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction, ICML, Proceedings of the 40th International Conference on Machine Learning, PMLR 202:12339-12350, 2023.
• 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, U. Etayo, B. Gariboldi, G. Gigante, T. Peter: Asymptotically optimal cubature formulas on manifolds for prefixed weights, (sciencedirect) J. Approx. Theory, 271, 105632, 2021. 
• 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, G. Ramos Llorden, et al.: Orthogonal projections for image quality analyses applied to MRI, (Nature) Proceedings in Applied Mathematics and Mechanics, Vol 20, 2021.
• 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, (Springer) Journal of Mathematical Imaging and Vision (JMIV)  vol. 62, 376-394 (2020) 
• J. I. Orlando, B. S. Gerendas, et al., Automated Quantification of Photoreceptor alteration in macular disease using Optical Coherence Tomography and Deep Learning, (Nature) Nature Scientific Reports, 10, 5619 (2020).