Publications

  1. M. Ehler, K. Gröchenig: t-design curves and mobile sampling on the sphere, arXiv 2023.
  2. M. Ehler, K. Gröchenig: Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities, arXiv 2022.
  3. A. Breger, C. Karner, M. Ehler: visClust: A visual clustering algorithm based on orthogonal projections, arXiv, 2022.
  4. 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.
  5. 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.
  6. 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).
  7. 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. 
  8. M. Ehler, M. Gräf, S. Neumayer, G. Steidl: Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization, (Springer) Found. Comput. Math. 2021 
  9. 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.
  10. 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) 
  11. 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).
  12. A. Breger, J. I. Orlando, et al.: An amplified-target loss approach for photoreceptor layer segmentation in pathological OCT scans, (arXiv:1908.00764) Springer Lecture Notes in Computer Science (MICCAI), 2019.
  13. M. Ehler, S. Kunis, T. Peter, C. Richter: A Randomized Multivariate Matrix Pencil Method for Superresolution Microscopy, (ETNA) Electronic Transactions on Numerical Analysis vol. 51, (2019), 63-74. 
  14. M. Ehler, M. Gräf, C. J. Oates: Optimal Monte Carlo integration on closed manifolds, (Springer) Statistics and Computing vol 29 (2019), no. 6, 1203-1214. 
  15. M. Ehler, M. Gräf: Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians, (Springer) Constr. Approx., vol. 49 (2018), no. 1, 29-58. 
  16. A. Breger, M. Ehler, M. Gräf: Points on manifolds with asymptotically optimal covering radius, (arXiv:1607.06899) Journal of Complexity 2018. 
  17. 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. 
  18. B. G. Bodmann, M. Ehler, M. Gräf: From low to high-dimensional moments without magic, (Springer) J. Theor. Probab., (2017) 
  19. 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, (Nature) 
    Eye, Springer Nature, 2017. 
  20. F. Bachoc, M. Ehler, M. Gräf: Optimal configurations of lines and a statistical application, (Springer) Advances in Computational Mathematics, vol. 43, no. 1, (2017), 113-126.
  21. 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)
  22. M. Ehler, M. Gräf: Numerically optimizing weights for Monte Carlo integration on smooth compact manifolds, 19th International Symposium on Symbolic and Numeric Algorithms for Scientifc Computing, 2017 (arXiv:1707.04723) 
  23. A. Breger, M. Ehler: Sampling in Grassmannians (IEEE) SampTA 2017, Sampling Theorie and Applications, Tallinn.
  24. A. Breger, M. Ehler, M. Gräf, T. Peter: Cubatures on Grassmannians: moments, dimension reduction, and related topics, (Publisher) Compressed Sensing and its Applications: MATHEON Workshop 2015 (Applied and Numerical Harmonic Analysis), 2017.
  25. 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, 2016.
  26. M. Ehler, M. Gräf, F. Király: Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices, (journal) Waves, Wavelets and Fractals – Advanced Analysis, vol. 1, no. 1 (2015). 
  27. M. Ehler: Preconditioning filter bank decompositions using structured normalized tight frames, (arXiv:1305.0716) J. Appl. Math. (2015) 
  28. 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. 
  29. M. Ehler, J. Dobrosotskaya, et al.: Modeling photo-bleaching kinetics to create high resolution maps of rod rhodopsin in the human retina, (PLoS ONE)
    PLoS ONE, vol. 10 (2015), no. 7, e0131881. 
  30. 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.
  31. M. Ehler, F. Filbir: Wavelet frames to optimally learn functions on diffusion measure spaces, 
    9th International ISAAC Congress, 2015, 715-720.
  32. 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). 
  33. 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.
  34. 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.
  35. C. Bachoc, M. Ehler: Tight p-fusion frames, (arXiv:1201.1798)
    Appl. Comput. Harmon. Anal. vol. 35 (2013), no. 1, 1-15.
  36. J. J. Benedetto, W. Czaja, M. Ehler: Wavelet Packets for time-frequency analysis of multi-spectral images, (Springer) International Journal on Geomathematics (GEM), vol. 4 (2013), 137-154.
  37. M. Ehler: Modifications of iterative schemes used for curvature correction in noninvasive noncontact biomedical imaging, (JBO) J. Biomed. Optics, vol. 18 (2013), no. 10, 100503.
  38. M. Ehler, K. Okoudjou: Probabilistic frames: An overview, (arXiv) arXiv:1108.2169v1
    Finite Frames: Theory and Applications, Eds.: P. G. Casazza and G. Kutyniok, Birkhauser, Series in Applied and Numerical Harmonic Analysis, 2013
  39. M. Ehler, S. Kunis: Phase retrieval using finitely many nonequispaced Fourier measurements, (EURASIP) SampTA 2013 .
  40. M. Ehler: Random tight frames, (arXiv) J. Fourier Anal. Appl. vol. 18 (2012), no. 1, 1-20
  41. M. Ehler, K. Okoudjou: Minimization of the p-th probabilistic frame potential, (arXiv) 
    J. Statist. Plann. Inference, vol. 142 (2012), no. 3, 645-659.
  42. M. Ehler, F. Filbir, H. Mhaskar: Locally learning biomedical data using diffusion frames, (ncbi) J. Comput. Biol. vol. 19 (2012), no. 11, 1251-64.
  43. M. Ehler, M. Hirn: Sparse endmember extraction and demixing, IEEE Geoscience and Remote Sensing Symposium, IGARSS (2012), Munich.
  44. M. Ehler, J. Dobrosotskaya, E. J. King, R. F. Bonner, Quantification of retinal chromophores through autofluorescence imaging to identify precursors of age-related macular degeneration,
    Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center, Eds.: T. Andrews, R. Balan, J. J. Benedetto, W. Czaja, K. A. Okoudjou, Springer, 2012
  45. M. Ehler, F. Filbir, H. N. Mhaskar: Learning biomedical data locally using diffusion geometry techniques,
    IASTED Imaging and Signal Processing in Health Care and Technology (2012).
  46. M. Ehler: Shrinkage rules for variational minimization problems and applications to analytical ultracentrifugation, (pdf)
    J. Inverse Ill-Posed Probl., vol. 19 (2011), no. 4-5, 593-614
  47. M. Ehler, J. Galanis: Frame theory in directional statistics, (pdf)
    Stat. Probabil. Lett., vol. 81 (2011), no. 8, 1046-1051.
  48. J. Kainerstorfer, J. D. Riley, M. Ehler, et al.: Quantitative principal component model for skin chromophore mapping using multi spectral images and spatial priors, (pdf)
    Biomed. Opt. Express vol. 2 (2011), no. 5, 1040-1058.
  49. M. Ehler, J. Kainerstorfer, D. Cunningham, et al.: An extended correction model for optical imaging,
    IEEE International Conference on Computational Advances in Bio and Medical Sciences, (2011), 93-98.
  50. M. Ehler, V. N. Rajapakse, et al.: Nonlinear gene cluster analysis with labeling for microarray gene expression data in organ development, (pdf)
    BMC Proceedings, vol. 5(Suppl 2) (2011), S3.
  51. B. R. Zeeberg, H. Liu, A. Kahn, M. Ehler, et al.: RedundancyMiner: De-replication of redundant GO categories in microarray and proteomics analysis, (pdf)
    BMC Bioinformatics, vol. 12 (2011), no. 52.
  52. J. Galanis, M. Ehler: Disorder Disguised as Order: the Science of Randomness, (pdf)
    Proceedings of the 14th Generative Art International Conference 2011, Rome.
  53. J. Dobrosotskaya, M. Ehler, et al.: Modeling of the rhodopsin bleaching with variational analysis of retinal images, (pdf)
    SPIE Medical Imaging, Image Processing, vol. 7962, 2011.
  54. M. Ehler, J. Dobrosotskaya, et al., Modeling photo-bleaching kinetics to map local variations in rod rhodopsin density, (pdf)
    SPIE Medical Imaging, Computer-Aided Diagnosis vol. 7963, 2011.
  55. M. Ehler: The minimal degree of solutions to polynomial equations used for the construction of refinable functions, (pdf)
    Sampl. Theory Signal Image Process., vol. 9 (2010), no. 1-3, 155-165.
  56. M. Ehler: The multiresolution structure of pairs of dual wavelet frames for a pair of Sobolev spaces, (pdf)
    Jaen J. Approx., vol. 2 (2010), no. 2, 193-214.
  57. M. Ehler and K. Koch: The construction of multiwavelet bi-frames and applications to variational image denoising, (pdf)
    Int. J. Wavelets, Multiresolut. Inf. Process., vol. 8 (2010), no. 3, 431-455.
  58. J. Kainerstorfer, F. Amyot, M. Ehler, et al.: Direct curvature correction for non-contact imaging modalities – applied to multi-spectral imaging, (pdf)
    J. Biomed. Optics, vol. 15 (2010).
  59. J. Kainerstorfer, M. Ehler, et al.: Principal component model of multi-spectral data for near real-time skin chromophore mapping, (pdf)
    J. Biomed. Optics, vol. 15 (2010).
  60. M. Ehler, V. N. Rajapakse, et al.: Analysis of temporal-spatial co-variation within gene expression microarray data in an organogenesis model, (pdf)
    Springer Verlag Lecture Notes in Bioinformatics, 6th International Symposium on Bioinformatics Research and Applications(2010).
  61. M. Ehler, B. P. Brooks, and R. F. Bonner: Directional equilibrium of gene regulatory networks in developmental biology,
    International Conference on Bioinformatics & Computational Biology, Las Vegas (2010).
  62. J. J. Benedetto, W. Czaja, and M. Ehler: Frame potential classification algorithm for retinal data, (pdf)
    Springer Proceedings Series: Intern. Fed. for Medical & Biological Engineering, 26th Southern Biomedical Engineering Conference (2010).
  63. J. Dobrosotskaya, M. Ehler, et al.: Sparse representation and variational methods in retinal image processing, (pdf)
    Springer Proceedings Series: Intern. Fed. for Medical & Biological Engineering, 26th Southern Biomedical Engineering Conference (2010).
  64. M. Ehler, Z. Majumdar, et al.: High-resolution autofluorescence imaging for mapping molecular processes within the human retina, (pdf)
    Springer Proceedings Series: Intern. Fed. for Medical & Biological Engineering, 26th Southern Biomedical Engineering Conference (2010).
  65. J. J. Benedetto, W. Czaja, M. Ehler, C. Flake, and M. Hirn: Wavelet Packets for multi- and hyper-spectral imagery, (SPIE) IS&T/SPIE Electronic Imaging 2010, Wavelet Applications in Industrial Processing VII, 7535 (2010).
  66. J. Kainerstorfer, F. Amyot, M. Hassan, M. Ehler, et al.: Reconstruction-free imaging of Kaposi’s Sarcoma using multi-spectral data, (optica) Biomedical Optics (BIOMED), Imaging and Spectroscopy Theory (2010).
  67. M. Ehler: Nonlinear approximation associated with nonseparable wavelet bi-frames, (sciencedirect) J. Approx. Theory. vol. 161 (2009), no. 1, 292-313.
  68. M. Ehler and S. Geisel: Arbitrary shrinkage rules for approximation schemes with sparsity constraints, (pdf) Schloss Dagstuhl Seminar Proceedings – Structured Decompositions and Efficient Algorithms, no. 08492, (2009), (Stephan Dahlke, Ingrid Daubechies, Michal Elad, Gitta Kutyniok, and Gerd Teschke, editors) Leibniz-Zentrum fuer Informatik, Germany, http://drops.dagstuhl.de/opus/volltexte/2009/1881/
  69. M. Ehler and B. Han: Wavelet bi-frames with few generators from multivariate refinable functions, (Springer) Appl. Comput. Harmon. Anal., vol. 25 (2008), no. 3, 407-414.
  70. M. Ehler: Compactly supported multivariate pairs of dual wavelet frames obtained by convolution, (doi) Int. J. Wavelets, Multiresolut. Inf. Process., vol. 6 (2008), no. 2, 183-208.
  71. M. Ehler: On multivariate compactly supported bi-frames, (Springer) J. Fourier Anal. Appl., vol. 13 (2007), no. 5, 511-532.
  72. M. Ehler: The Construction of Nonseparable Wavelet Bi-Frames and Associated Approximation Schemes, (Logos Verlag), (uni-marburg) Logos Verlag (2007), Berlin.