358 citations · 1.1k across the 35 of their papers we have counts for
38 papers
Convergence Rates for Oversmoothing Banach Space Regularization
Philip Miller, Thorsten Hohage
This paper studies Tikhonov regularization for finitely smoothing operators in Banach spaces when the penalization enforces too much smoothness in the sense that the penalty term i…
Learned infinite elements
Thorsten Hohage, Christoph Lehrenfeld, Janosch Preuss
We study the numerical solution of scalar time-harmonic wave equations on unbounded domains which can be split into a bounded interior domain of primary interest and an exterior do…
A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem
Thorsten Hohage, Frédérique Le Louër
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is so…
On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations
Martin Halla, Thorsten Hohage
We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms thes…
Maximal Spaces for Approximation Rates in -regularization
Philip Miller, Thorsten Hohage
We study Tikhonov regularization for possibly nonlinear inverse problems with weighted -penalization. The forward operator, mapping from a sequence space to an arbitrary Ba…
Weighted Data Spaces for Correlation-Based Array Imaging in Experimental Aeroacoustics
Hans-Georg Raumer, Carsten Spehr, Thorsten Hohage +1
This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation…
Sweeping preconditioners for stratified media in the presence of reflections
Janosch Preuß, Thorsten Hohage, Christoph Lehrenfeld
In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sw…
Uniqueness of an inverse source problem in experimental aeroacoustics
Thorsten Hohage, Hans-Georg Raumer, Carsten Spehr
This paper is concerned with the mathematical analysis of experimental methods for the estimation of the power of an uncorrelated, extended aeroacoustic source from measurements of…
Global uniqueness in a passive inverse problem of helioseismology
A. D. Agaltsov, T. Hohage, R. G. Novikov
We consider the inverse problem of recovering the spherically symmetric sound speed, density and attenuation in the Sun from the observations of the acoustic field randomly excited…
Density Matrix Reconstructions in Ultrafast Transmission Electron Microscopy: Uniqueness, Stability, and Convergence Rates
Cong Shi, Claus Ropers, Thorsten Hohage
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem…
Elastic energy regularization for inverse obstacle scattering problems
Julian Eckhardt, Ralf Hiptmair, Thorsten Hohage +2
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bend…
Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces
Thorsten Hohage, Philip Miller
This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on penalty terms which y…
The imaginary part of the scattering Green function: monochromatic relations to the real part and uniqueness results for inverse problems
Alexey Agaltsov, Thorsten Hohage, Roman Novikov
For many wave propagation problems with random sources it has been demonstrated that cross correlations of wave fields are proportional to the imaginary part of the Green function…
Higher order convergence rates for Bregman iterated variational regularization of inverse problems
Benjamin Sprung, Thorsten Hohage
We study the convergence of variationally regularized solutions to linear ill-posed operator equations in Banach spaces as the noise in the right hand side tends to . The rate o…
Problems in computational helioseismology
Laurent Gizon, Damien Fournier, Thorsten Hohage
We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction a…
Attosecond Electron Pulse Trains and Quantum State Reconstruction in Ultrafast Transmission Electron Microscopy
Katharina E. Priebe, Christopher Rathje, Sergey V. Yalunin +4
We introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond pulse trains for e…
Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows
Laurent Gizon, Hélène Barucq, Marc Duruflé +7
Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are…
Stability estimates for linearized near-field phase retrieval in X-ray phase contrast imaging
Simon Maretzke, Thorsten Hohage
Propagation-based X-ray phase contrast enables nanoscale imaging of biological tissue by probing not only the attenuation, but also the real part of the refractive index of the sam…
Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods
Thorsten Hohage, Frederic Weidling
We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree…
Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
Frederic Weidling, Thorsten Hohage
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic wav…
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Simon Maretzke, Matthias Bartels, Martin Krenkel +2
Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an…
Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
Claudia König, Frank Werner, Thorsten Hohage
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain…
Pinsker estimators for local helioseismology
D. Fournier, L. Gizon, M. Holzke +1
A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time mea…
Verification of a variational source condition for acoustic inverse medium scattering problems
Thorsten Hohage, Frederic Weidling
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic ac…