Edited Book

  • Handbook of Variational Methods for Nonlinear Geometric Data (with P. Grohs and M. Holler), Springer Nature, 2020.

Articles in Journals

2021

  • Clothoid fitting and geometric Hermite subdivision (with U. Reif). Advances in Computational Mathematics 47 (2021), to appear.
  • Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case (with L. Kiefer and M. Storath). Foundations of Computational Mathematics 21 (2021), 649-694.
  • Multi-channel Potts-based reconstruction for multi-spectral computed tomography (with L. Kiefer, S. Petra, and M. Storath). Inverse Problems 37 (2021), 045004.
  • Variational regularization of inverse problems for manifold-valued data (with M. Storath). Information and Inference 10 (2021), 195–230.

2020

  • PALMS Image Partitioning – A New Parallel Algorithm for the Piecewise Affine-Linear Mumford-Shah Model
    (with L. Kiefer and M. Storath). Image Processing On Line 10 (2020), 124-149.
  • An Algorithm for Second Order Mumford–Shah Models Based on a Taylor Jet Formulation (with L. Kiefer, and M. Storath), SIAM Journal on Imaging Sciences 13 (2020), 2307-2360.
  • Wavelet sparse regularization for manifold-valued data (with M. Storath), Multiscale Modeling & Simulation 18 (2020), 674-706.

2019

  • Smoothing for signals with discontinuities using higher order Mumford–Shah models (with M. Storath, and L. Kiefer),  Numerische Mathematik 143 (2019), 423-460.
  • An efficient algorithm for the piecewise affine-linear Mumford-Shah model based on a Taylor jet splitting
     (with L. Kiefer and M. Storath), IEEE Transactions on Image Processing 29 (2019), 921-933.
  • Total variation regularization of pose signals with an application to 3D freehand ultrasound (with M Esposito et al.). IEEE Transactions on Medical Imaging 38 (2019), 2245-2258.

2018

  • Fast piecewise-affine motion estimation without segmentation (with D. Fortun, M. Storath, D. Rickert, and M. Unser). IEEE Transactions on Image Processing 27 (2018), 5612-5624.
  • Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging
    (with W. Erb et al.) Inverse Problems 34 (2018), 055012.
  • Total generalized variation for manifold-valued data (with K. Bredies, M. Holler, and M. Storath). SIAM Journal on Imaging Sciences 11 (2018), 1785-1848.
  • Model-based learning of local image features for unsupervised texture segmentation (with M. Kiechle, M. Storath, and M. Kleinsteuber). IEEE Transactions on Image Processing 27 (2018), 1994-2007.

2017

  • Fast median filtering for phase or orientation data (with M. Storath). IEEE Transactions on Pattern Analysis and Machine Intelligence 40 (2017), 639-652.
  • Fast segmentation from  blurred data in 3D~fluorescence microscopy (with M. Storath, D. Rickert, and M. Unser). IEEE Transactions on Image Processing, 26 (2017), 4856–4870.
  • Jump-penalized least absolute values estimation of scalar or circle-valued signals (with M. Storath and M. Unser). IMA Inference and Information 6 (2017), 225–245.
  • Edge preserving and noise reducing reconstruction for magnetic particle imaging (with M. Storath, C. Brandt, M. Hofmann, T. Knopp, J. Salomon, and A. Weber). IEEE Transactions on Medical Imaging 36 (2017), 74-85.

2016

  • Model-based reconstruction for magnetic particle imaging in 2D and 3D (with T. Maerz). Inverse Problems and Imaging 10 (2016), 1087-1110.
  • Joint segmentation and shape regularization with a generalized forward backward algorithm (with A. Stefanoiu, M. Storath, N. Navab, M. Baust). IEEE Transactions on Image Processing 25 (2016), 3384-3394.
  • Combined tensor fitting and TV regularization in diffusion tensor imaging based on a Riemannian manifold approach (with M. Baust,  M. Wieczorek, T. Lasser, M. Storath, N. Navab). IEEE Transactions on Medical Imaging 35 (2016), 1972-1989.
  • A second order non-smooth variational model for restoring manifold-valued images (with M. Bacak, R. Bergmann, and G. Steidl). SIAM Journal on Scientific Computing 38 (2016), A567–A597.
  • Exact algorithms for L1-TV regularization of real-valued or circle-valued signals  (with M. Storath and M. Unser). SIAM Journal on Scientific Computing 38 (2016), A614–A630. Preprint.
  • A second order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data (with R. Bergmann).  Journal of Mathematical Imaging and Vision 55 (2016), 401-427.
  • Mumford-Shah  and Potts regularization for manifold-valued data (with L. Demaret and M. Storath). Journal of Mathematical Imaging and Vision 55 (2016): 428-445. Preprint.

2015

  • An algorithmic framework for Mumford-Shah regularization of inverse problems in imaging (with K. Hohm and M. Storath). Inverse Problems 31 (2015) , 115011.
  • Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements (with M. Storath). Proceedings of the Royal Society A 471 (2015), 20140638.
  • The L1-Potts functional for robust jump-sparse reconstruction (with M. Storath and L. Demaret). SIAM Journal on Numerical Analysis 53 (2015), 644-673. Preprint.
  • Second order differences of cyclic data and applications in variational denoising (with R. Bergmann, F. Laus and G. Steidl). SIAM Journal on Imaging Sciences (2014), 2916-2953.  Preprint.
  • Joint image reconstruction and segmentation using the Potts model  (with M. Storath, J. Frikel and M. Unser ). Inverse Problems 31 (2015), 025003. Preprint.

2014 and before

  • Total variation regularization for manifold-Valued data (with L. Demaret and M. Storath). SIAM Journal on Imaging Sciences 7 (2014), 2226-2257. Preprint.
  • Fast partitioning of vector-valued images (with M. Storath). SIAM Journal on Imaging Sciences 7 (2014), 1826-1852. Preprint.
  • Jump-sparse and sparse recovery using Potts functionals (with M. Storath and L. Demaret).   IEEE Transactions on Signal Processing 62 (2014), 3654-3666. Preprint.
  • Interpolatory multiscale representation for functions between manifolds. SIAM Journal on Mathematical Analysis 44 (2012), 162-191. Preprint.
  • Subdivision schemes with general dilation in the geometric and nonlinear setting. Journal of Approximation Theory 164 (2012),  105-137. Preprint.
  • Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces (with J. Wallner and E. Nava Yazdani). Advances in Computational Mathematics 34 (2011), 201-218. Preprint.
  • Lipschitz spaces with respect to Jacobi translation (with R. Lasser). Mathematische Nachrichten 284 (2011), 2312-2326. Preprint.
  • Nonlinear subdivision schemes on irregular meshes. Constructive Approximation 31 (2010), 395-415. Preprint.

Book Chapters

  • Non-smooth variational regularization for processing manifold-valued data (with M. Holler). Springer Handbook of Variational Methods for Nonlinear Geometric Data,  51-93 (2020).
  • Manifold-Valued Data in Medical Imaging Applications (with M. Baust). Springer Handbook of Variational Methods for Nonlinear Geometric Data, 613-647 (2020).

Articles in Conference Proceedings

  • Direct MRI Segmentation from k-Space Data by Iterative Potts Minimization (with L. Kiefer, S. Petra, and M. Storath). International Conference on Scale Space and Variational Methods, 2019.
  • Total variation regularization of shape signals  (with M. Baust, L. Demaret, M. Storath, and N. Navab). IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2015.
  • Inpainting of cyclic data using first and second order differences (with R. Bergmann).  Proceedings of the Conference on Energy Minimization in Computer Vision and Pattern Recognition 2015. Pages 155–168. Preprint.
  • Unsupervised texture segmentation using monogenic curvelets and the Potts model (with M. Storath and M. Unser). Proceedings of the IEEE International Conference on Image Processing (ICIP) 2014. Pages 4348–4352.