M26. Variational Methods for Inverse Problems in Imaging

Variational methods nowadays rank among the most powerful and flexible approaches to tackle inverse problems in imaging. These include real-world applications like magnetic resonance imaging, positron emission tomography, computer tomography, transmission electron microscopy and many other recovery problems in medicine, engineering, and life sciences. Further, variational methods have proven themselves highly valuable for data pre-processing and image post-processing such as denoising, deblurring and inpainting. The recent years have seen several new developments in this area, coming from different mathematical backgrounds and being applicable for a variety of inverse problems. These developments include, for instance, deep learning approaches, tensorial lifting strategies, as well as novel optimal-transport- and total-variation-based regularizers. On the other hand, new techniques such as deep neural networks for inverse problems are inspired by variational methods. The aim of this minisymposium is to bring together experts with various backgrounds to discuss these recent achievements in the context of inverse problems in imaging, and to initiate potential new research directions and collaborations.

Organizers:
Robert Beinert, University of Graz, Austria, This email address is being protected from spambots. You need JavaScript enabled to view it.
Kristian Bredies, University of Graz, Austria, This email address is being protected from spambots. You need JavaScript enabled to view it.

Speakers (in alphabetical order):
Robert Beinert, University of Graz, Austria, This email address is being protected from spambots. You need JavaScript enabled to view it.
Solving masked phase retrieval by tensorial liftings and tensor-free algorithms

Benjamin Berkels, RWTH Aachen University, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
Joint exit wave reconstruction and image registration as a least-squares problem

Tatiana Bubba, University of Helsinki, Finland, This email address is being protected from spambots. You need JavaScript enabled to view it.
Limited angle tomography: inpanting in phase space by deep learning

Birgit Komander, TU Braunschweig, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
Denoising of image gradients and total generalized variation

Jean-Christophe Pesquet, University Paris-Saclay, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
Proximal-interior point strategies in image recovery

Rudolf Stollberger, TU Graz, Austria, This email address is being protected from spambots. You need JavaScript enabled to view it.
Variational methods for functional and quantitative MRI

Robert Tovey, National Institute for Research in Computer Science and Control, INRIA, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
A variational method for joint denoising-reconstruction with directional total-variation regularization


PLENARY SPEAKERS

Prof. Dr. Liliana Borcea

University of Michigan, USA
http://www-personal.umich.edu/~borcea/

Inverse scattering in random media, Electro-magnetic inverse problems, Effective properties of composite materials, transport in high contrast, heterogeneous media

Prof. Dr. Bernd Hofmann

Chemnitz University of Technology, Germany
https://www.tu-chemnitz.de/mathematik/inverse_probleme/hofmann/?en=1

Regularization of inverse and ill-posed problems

Prof. Dr. John C Schotland

Yale University, USA
https://gauss.math.yale.edu/~js4228/

Inverse problems with applications to imaging, Scattering theory, Waves in random media, Nano-scale optics, Coherence theory and quantum optics

Prof. Dr. Erkki Somersalo

Case Western Reserve University, USA
https://mathstats.case.edu/faculty/erkki-somersalo/

Computational and statistical inverse problems, Probabilistic methods for uncertainty quantification, Modeling of complex systems, Biomedical applications

Prof. Dr. Gunther Uhlmann

University of Washington, USA
https://sites.math.washington.edu/~gunther/

Inverse problems and imaging, Partial differential equations, Microlocal analysis, Scattering theory

Prof. Dr. Jun Zou

The Chinese University of Hong Kong, Hong Kong SAR
https://www.math.cuhk.edu.hk/~zou/

Numerical solutions of electromagnetic Maxwell systems and interface problems, inverse and ill-posed problems, preconditioned and domain decomposition methods