13 citations · 56 across the 16 of their papers we have counts for
18 papers
Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
Clemens Kirisits, Bochra Mejri, Sergei Pereverzev +2
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incor…
Using the Transport of Intensity and the Transport of Phase Equation for Phase Retrieval
Clemens Kirisits, Kemal Raik, Otmar Scherzer +2
We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived fro…
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…
Diffraction Tomography for a Generalized Incident Field
Clemens Kirisits, Noemi Naujoks, Otmar Scherzer
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is expos…
Uncertainty Quantification for Scale-Space Blob Detection
Fabian Parzer, Clemens Kirisits, Otmar Scherzer
We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical app…
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…
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…
A range condition for polyconvex variational regularization
Clemens Kirisits, Otmar Scherzer
In the context of convex variational regularization it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequaliti…
Convergence rates for regularization functionals with polyconvex integrands
Clemens Kirisits, Otmar Scherzer
Convergence rates results for variational regularization methods typically assume the regularization functional to be convex. While this assumption is natural for scalar-valued fun…
Convective regularization for optical flow
José A. Iglesias, Clemens Kirisits
We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity fie…
Optical Flow on Moving Manifolds
Martin Bauer, Markus Grasmair, Clemens Kirisits
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional…
Decomposition of Optical Flow on the Sphere
Clemens Kirisits, Lukas F. Lang, Otmar Scherzer
We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the -sphere. While motion estimation is based on the optical f…
Optical Flow on Evolving Surfaces with Space and Time Regularisation
Clemens Kirisits, Lukas F. Lang, Otmar Scherzer
We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images.…
Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data
Clemens Kirisits, Lukas F. Lang, Otmar Scherzer
We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to…
Total Variation Denoising on Hexagonal Grids
Clemens Kirisits
This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact grap…