Abstract : Inverse problems are concerned with determining unknown parameters of interest from indirect, partial, and noisy measurements with the aid of a mathematical model. Such problems are fundamental in biomedical imaging, non-destructive testing, and modern astronomy. Often, these parameters take the form of images rather than scalar or vector-valued parameters, requiring special methods adapted to the distributed structure. The aim of this minisymposium is to gather an active group of researchers working on variational methods for solving inverse and imaging problems, in order to foster increased interaction between these fields and those of applications in science, technology, and industry.
[01259] Testing statistical hypothesis in Inverse Problems
Format : Talk at Waseda University
Author(s) :
Frank Werner (Universität Würzburg)
Remo Kretschmann (Universität Würzburg)
Daniel Wachsmuth (Universität Würzburg)
Abstract : In this talk, we propose a regularized approach to hypothesis testing in Inverse Problems in the sense that the underlying estimators or test statistics are allowed to be biased. As one major result we prove that regularized testing is always at least as good as classical unregularized testing. We furthermore provide an adaptive test by maximizing the power functional, which outperforms unregularized tests in numerical simulations by several orders of magnitude.
[01346] Disentangling domain bias in medical images for meaningful embeddings
Format : Talk at Waseda University
Author(s) :
Samuel Tull (University of Cambridge)
Abstract : Machine learning models using imaging have been promising to revolutionise healthcare for many years but are rarely deployed in the clinic due to underlying dataset biases and distribution shifts. In medical images, several sources of bias cause a distribution shift: image acquisition protocols, the instrument used and any image processing. We discuss a method giving meaningful image embeddings, useful for downstream tasks, that have been disentangled from sources of bias, achieving improved generalisability and interpretability.
[01553] A Bregman-Kaczmarz method for nonlinear systems of equations
Format : Talk at Waseda University
Author(s) :
Maximilian Winkler (TU Braunschweig)
Abstract : We propose a new randomized method for solving systems of nonlinear equations for sparse solutions or solutions which are subject to simple additional constraints. The method uses only gradients of component functions and is based on Bregman projections. Convergence is established for convex nonnegative functions and for functions that fulfill the local tangential cone condition. We demonstrate in examples that the method can find sparse or simplex-constrained solutions of inverse problems.
[01556] A complementary $\ell^1$-TV reconstruction algorithm for limited data CT
Format : Talk at Waseda University
Author(s) :
Simon Goeppel (University of Innsbruck)
Jürgen Frikel (OTH Regensburg)
Markus Haltmeier (University of Innsbruck)
Abstract : In this talk, we introduce a new variational reconstruction framework for inverse problems, suffering from incomplete data. As it is known that a single regularizer does not work flawlessly for noise reduction and artifact removal simultaneously, we instead adress both problems by subsequent reconstructions. These reconstructions are connected by a data-consistency term, which enables us to uitilize both properties of $\ell_1$-curvelet and total variation regularization in the example of limited angle tomography.
[01577] 3D image reconstruction for cone beam computed tomography using sparsity
Format : Talk at Waseda University
Author(s) :
Alexander Meaney (University of Helsinki)
Samuli Siltanen (University of Helsinki)
Abstract : Cone beam computed tomography is an increasingly popular three-dimensional medical imaging technique. However, in many settings it suffers from suboptimal image quality. In this work, we will present a new approach to regularized iterative image reconstruction. Our technique has an in-built automatic choice of the regularization parameter, based on a priori knowledge on gradient sparsity. Combined with a novel primal-dual optimization algorithm, this results in an efficient technique for large-scale reconstruction of improved quality.
[01591] High Dynamic Range Tomography via Modulo Radon Transform
Format : Talk at Waseda University
Author(s) :
Matthias Beckmann (University of Bremen)
Abstract : Recently, practitioners in tomography proposed high dynamic range solutions that are inspired by multi-exposure fusion strategies in computational photography. In this talk, we propose a single-shot alternative based on the novel Modulo Radon Transform, which folds Radon projections via modulo non-linearity into the dynamic range of the sensor to avoid information loss due to saturation. We propose a sequential reconstruction algorithm, which is backed by mathematical guarantees, and illustrate our theoretical results by numerical simulations.
[01593] A new inversion scheme for elastic diffraction tomography
Author(s) :
Bochra Mejri (RICAM, Austria Johann Radon Institute for Computational and Applied Mathematics)
Otmar Scherzer (University of Vienna)
Abstract : We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties, i.e. mass density and elastic Lamé parameters, of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization
using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the 2D
Fourier transform of scattered waves with the Fourier transform of the scatterer in the 3D spatial Fourier domain.
Elastic wave mode separation is performed, which decomposes a wave into four modes. A new two-step inversion
process is developed, providing information on the modes first and secondly on the elastic parameters. Finally, we
discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different
plane wave excitation frequencies, respectively.
[01606] inverse electromagnetic scattering problems with internal dipoles
Format : Talk at Waseda University
Author(s) :
Yakun Dong (University of Vienna)
Otmar Scherzer (University of Vienna)
Kamran Sadiq (Radon Institute for Computational and Applied Mathematics)
Abstract : We propose a method to reconstruct the optical properties of inverse scattering problems with internal sources. The method is based on macroscopic Maxwell’s equations and achieves super-resolution reconstruction. Applications in single-molecule localization microscopy are shown.
[03917] A paraxial approach for the inverse problem of vibroacoustic imaging
Format : Talk at Waseda University
Author(s) :
Teresa Rauscher (University of Klagenfurt)
Abstract : Vibroacoustography by means of ultrasound is an imaging method that was developed to achieve higher resolutions while avoiding the drawbacks of scattering and stronger attenuation. High frequency waves that show a strongly preferred direction of propagation are sent into the medium. Therefore, we make use of a paraxial approach to arrive at a system of PDEs that involve space dependent parameters. In this talk, we will deal with the modeling and inverse problem for vibroacoustography.
[05513] Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
Format : Talk at Waseda University
Author(s) :
Christian Clason (University of Graz)
Stanislav Mazurenko (Masaryk University)
Tuomo Valkonen (EPN, Quito and University of Helsinki)
Abstract : We demonstrate that non-convex non-smooth optimization problems like the Potts segmentation model can be written in terms of generalized conjugates of convex functionals, which can be solved by a conceptually straightforward extension of the primal–dual proximal splitting method of Chambolle and Pock. We show convergence and illustrate these theoretical results numerically on the aforementioned example problem.
