Publications

Preprint

• Johannes Hertrich, Tim Jahn and Michael Quellmalz:
  Fast Summation of Radial Kernels via QMC Slicing
  ArXiv preprint 2410.01316. (pdf)

• Nicolaj Rux, Michael Quellmalz and Gabriele Steidl:
  Slicing of Radial Functions: a Dimension Walk in the Fourier Space
  ArXiv preprint 2408.11612. (pdf)

• Clemens Kirisits, Michael Quellmalz and Eric Setterqvist:
  Generalized Fourier Diffraction Theorem and Filtered Backpropagation for Tomographic Reconstruction
  ArXiv preprint 2407.01793. (pdf)

• Oleh Melnyk, Michael Quellmalz, Gabriele Steidl, Noah Jaitner, Jakob Jordan and Ingolf Sack:
  Time-Harmonic Optical Flow with Applications in Elastography
  ArXiv preprint 2405.15507. (pdf)

Articles

• Michael Quellmalz, Léo Buecher and Gabriele Steidl:
  Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group
  Journal of Mathematical Imaging and Vision 2024. doi:10.1007/s10851-024-01206-w (Open Access) (pdf)

• Michael Quellmalz, Peter Elbau, Otmar Scherzer and Gabriele Steidl:
  Motion Detection in Diffraction Tomography by Common Circle Methods
  Mathematics of Computation 93(346), pages 747–784, March 2024. doi:10.1090/mcom/3869
  ArXiv preprint 2209.08086. (pdf)

• Michael Quellmalz, Robert Beinert and Gabriele Steidl:
  Sliced Optimal Transport on the Sphere
  Inverse Problems 39(10), 105005 (34 pages), 2023. doi:10.1088/1361-6420/acf156
  ArXiv preprint 2304.09092. (pdf)

• Sophie Mildenberger and Michael Quellmalz:
  A double Fourier sphere method for d-dimensional manifolds
  Sampling Theory, Signal Processing, and Data Analysis 21, Article number: 23 (40 pages), 2023. doi:10.1007/s43670-023-00064-8 (Open Access) (pdf)

• Michael Quellmalz, Lukas Weissinger, Simon Hubmer, Paul Erchinger:
  A Frame Decomposition of the Funk-Radon Transform
  L. Calatroni, M. Donatelli, S. Morigi, M. Prato, M. Santacesaria (Eds.): Scale Space and Variational Methods in Computer Vision. SSVM 2023, pages 42-54. Lecture Notes in Computer Science, vol 14009. Springer, Cham, 2023. doi:10.1007/978-3-031-31975-4_4
  ArXiv preprint 2303.05179. (pdf)

• Florian Faucher, Clemens Kirisits, Michael Quellmalz, Otmar Scherzer and Eric Setterqvist:
  Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion
  In: Ke Chen, Carola B. Schönlieb, Xue-Cheng Tai, Laurent Younces (Eds.) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, pages 273-312. Springer, Cham, 2023. doi:10.1007/978-3-030-98661-2_115
  ArXiv preprint 2110.07921. (pdf)

• Robert Beinert and Michael Quellmalz:
  Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object
  Proceedings in Applied Mathematics & Mechanics, 22(1), 6 pages, 2023. doi:10.1002/pamm.202200135 (Open Access). (pdf)

• Robert Beinert and Michael Quellmalz:
  Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography
  SIAM Journal on Imaging Sciences 15(3), p. 1373-1399 (2022). doi:10.1137/22M1474382
  ArXiv preprint 2201.11579. (pdf)

• Fatima Antarou Ba and Michael Quellmalz:
  Accelerating the Sinkhorn Algorithm for Sparse Multi-Marginal Optimal Transport via Fast Fourier Transforms
  Algorithms 15(9) (2022), p. 311. doi:10.3390/a15090311 (Open Access). (pdf)

• Sophie Mildenberger and Michael Quellmalz:
  Approximation Properties of the Double Fourier Sphere Method
  Journal of Fourier Analysis and Applications 28(2), Article number 31 (2022). doi:10.1007/s00041-022-09928-4 (Open Access) (pdf)

• Stephan Dahlke, Filippo De Mari, Ernesto De Vito, Markus Hansen, Marzieh Hasannasab, Michael Quellmalz, Gabriele Steidl and Gerd Teschke:
  Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited
  Applied and Computational Harmonic Analysis 56 (2022), p. 123-149. doi:10.1016/j.acha.2021.08.003
  ArXiv preprint 2012.13460. (pdf)

• Clemens Kirisits, Michael Quellmalz, Monika Ritsch-Marte, Otmar Scherzer, Eric Setterqvist and Gabriele Steidl:
  Fourier Reconstruction for Diffraction Tomography of an Object Rotated Into Arbitrary Orientations
  Inverse Problems 37 (2021), 115002. doi:10.1088/1361-6420/ac2749 (Open Access). (pdf)

• Michael Quellmalz:
  The Funk-Radon transform for hyperplane sections through a common point
  Analysis and Mathematical Physics 10(38), 2020. doi:10.1007/s13324-020-00383-2 (Open Access). (pdf)

• Michael Quellmalz, Ralf Hielscher and Alfred K. Louis:
  The Cone-Beam Transform and Spherical Convolution Operators
  Inverse Problems 34 (2018) 105006. doi:10.1088/1361-6420/aad679
  ArXiv postprint 1803.10515. (pdf)

• Ralf Hielscher, Daniel Potts and Michael Quellmalz:
  An SVD in Spherical Surface Wave Tomography
  In: Bernd Hofmann, Antonio Leitao and Jorge P. Zubelli (Eds.). New Trends in Parameter Identification for Mathematical Models, p. 121-144, Birkhäuser Basel, 2018. doi:10.1007/978-3-319-70824-9_7
  ArXiv postprint 1706.05284. (pdf)

• Michael Quellmalz:
  A Generalization of the Funk–Radon Transform
  Inverse Problems 33 (2017) 035016. doi:10.1088/1361-6420/33/3/035016 (pdf)

• Ralf Hielscher and Michael Quellmalz:
  Reconstructing a Function on the Sphere from Its Means Along Vertical Slices
  Inverse Problems and Imaging 10(3), 2016. doi:10.3934/ipi.2016018 (pdf)

• Ralf Hielscher and Michael Quellmalz:
  Optimal Mollifiers for Spherical Deconvolution
  Inverse Problems 31 (2015) 085001. doi:10.1088/0266-5611/31/8/085001 (pdf)

Theses

• Michael Quellmalz:
  Inversion of the Circular Average Transform on the Sphere
  Diploma thesis, TU Chemnitz, 2014. (pdf)