16 citations · 105 across the 23 of their papers we have counts for
19 papers · 1 filter
A Discrete Radon Transform Based on the Area of Cube-Plane Intersection
Robert Beinert, Jonas Bresch, Michael Quellmalz
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an a…
Application and Evaluation of the Common Circles Method
Michael Quellmalz, Mia Kvåle Løvmo, Simon Moser +2
We investigate the application of the common circle method for estimating sample motion in optical diffraction tomography (ODT) of sub-millimeter sized biological tissue. When samp…
Fast Summation of Radial Kernels via QMC Slicing
Johannes Hertrich, Tim Jahn, Michael Quellmalz
The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random proje…
Slicing of Radial Functions: a Dimension Walk in the Fourier Space
Nicolaj Rux, Michael Quellmalz, Gabriele Steidl
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributi…
Generalized Fourier Diffraction Theorem and Filtered Backpropagation for Tomographic Reconstruction
Clemens Kirisits, Michael Quellmalz, Eric Setterqvist
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction…
Time-Harmonic Optical Flow with Applications in Elastography
Oleh Melnyk, Michael Quellmalz, Gabriele Steidl +3
In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special…
Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group
Michael Quellmalz, Léo Buecher, Gabriele Steidl
Sliced optimal transport, which is basically a Radon transform followed by one-dimensional optimal transport, became popular in various applications due to its efficient computatio…
Sliced Optimal Transport on the Sphere
Michael Quellmalz, Robert Beinert, Gabriele Steidl
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-…
A Frame Decomposition of the Funk-Radon Transform
Michael Quellmalz, Lukas Weissinger, Simon Hubmer +1
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of t…
A double Fourier sphere method for -dimensional manifolds
Sophie Mildenberger, Michael Quellmalz
The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently approximate it by a Fourier series, whic…
Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object
Robert Beinert, Michael Quellmalz
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus li…
Motion Detection in Diffraction Tomography by Common Circle Methods
Michael Quellmalz, Peter Elbau, Otmar Scherzer +1
The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an o…
Total variation-based reconstruction and phase retrieval for diffraction tomography
Robert Beinert, Michael Quellmalz
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations wit…
Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion
Florian Faucher, Clemens Kirisits, Michael Quellmalz +2
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by i…
Approximation properties of the double Fourier sphere method
Sophie Mildenberger, Michael Quellmalz
We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a function defined on the two-dim…
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations
Clemens Kirisits, Michael Quellmalz, Monika Ritsch-Marte +3
In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for in…
The Funk-Radon transform for hyperplane sections through a common point
Michael Quellmalz
The Funk-Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk…
The cone-beam transform and spherical convolution operators
Michael Quellmalz, Ralf Hielscher, Alfred K. Louis
The cone-beam transform consists of integrating a function defined on the three-dimensional space along every ray that starts on a certain scanning set. Based on Grangeat's formula…
An SVD in Spherical Surface Wave Tomography
Ralf Hielscher, Daniel Potts, Michael Quellmalz
In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transfo…