6 citations · 19 across the 10 of their papers we have counts for
10 papers
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…
Local Approximations, Real Interpolation and Machine Learning
Eric Setterqvist, Natan Kruglyak, Robert Forchheimer
We suggest a novel classification algorithm that is based on local approximations and explain its connections with Artificial Neural Networks (ANNs) and Nearest Neighbour classifie…
An Improved Nearest Neighbour Classifier
Eric Setterqvist, Natan Kruglyak, Robert Forchheimer
A windowed version of the Nearest Neighbour (WNN) classifier for images is described. While its construction is inspired by the architecture of Artificial Neural Networks, the unde…
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…
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…
Iterative TV minimization on the graph
Japhet Niyobuhungiro, Eric Setterqvist, Freddie Åström +1
We define the space of functions of bounded variation () on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to i…
Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy
Clemens Kirisits, Eric Setterqvist, Otmar Scherzer
A recent result by Lasica, Moll and Mucha about the -anisotropic Rudin-Osher-Fatemi model in asserts that the solution is piecewise constant on a rectilinear…
On the ROF Model in Rectilinear Anisotropy: Piecewise Constant Approximation and Universal Minimality
Clemens Kirisits, Eric Setterqvist
We prove that the distance between the minimizer of the -anisotropic Rudin-Osher-Fatemi (ROF) functional and its minimizer over the space of piecewise constant functi…
Invariant -minimal sets and total variation denoising on graphs
Clemens Kirisits, Otmar Scherzer, Eric Setterqvist
Total variation flow, total variation regularization and the taut string algorithm are known to be equivalent filters for one-dimensional discrete signals. In addition, the filtere…
Energy of taut strings accompanying Wiener process
Mikhail Lifshits, Eric Setterqvist
Let be a Wiener process. The function minmizing energy among all functions satisfying on an interval is…