News Archive

Talk: "On Some Inverse Problems: Boundary Data Completion and Buried Flaws Detection"

We kindly invite you to the talk "On Some Inverse Problems: Boundary Data Completion and Buried Flaws Detection" by Naima Ben Meghnia. Friday, Aug. 6th, 10:00am Vienna Time.

Online at:

This presentation focuses, on the one hand, on the reconstruction of missing boundary data using the fictitious domain decomposition technique for the heat equation via a new robust algorithm that exploits the dynamic in time and we investigate the convergence analysis. On the other hand, on the identification of cavities in the two-dimensional linear elasticity system from the knowledge of partially overdetermined boundary data using the topological sensitivity analysis. we obtain the explicit formula of the topological derivative taking the energy-gap and L2-gap as cost functions, then we compare both functionals numerically. Several numerical experiments are illustrated to highlight the robustness and the accuracy of these two approaches.

Workshop: "Tomographic Reconstructions and their Startling Applications"

We are inviting to the Workshop "Tomographic Reconstructions and their Startling Applications" at the Erwin Schrödinger Institute for Mathematics and Physics (ESI) from March 15 until March 26. Due to the current restrictions, the conference will be held as an online event.

The workshop is organized within the interdisciplinary research program "Tomography Across the Scales" and is centered around the mathematical and experimental problems related to the applications studied in this project, involving adaptive optics, optical coherence tomography, photoacoustics, and superresolution imaging.

Talk: "Regularising linear inverse problems under unknown non-Gaussian noise"

We kindly invite you to the talk "Regularising linear inverse problems under unknown non-Gaussian noise" by Tim Jahn. Wednesday, Jan. 27th, 13:00 Vienna Time.

Online at:

We deal with the solution of linear ill-posed equations in Hilbert spaces. Usually, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications such ad hoc knowledge may often be unrealistic. However, the error of a measurement may often be estimated through averaging of repeated measurements. We combine this with classical Filter-based regularisation methods for a purely data-driven regularisation scheme. We obtain convergence to the true solution, with the only assumption that the measurements are unbiased, independent and identically distributed according to an elseways arbitrary unknown distribution (with finite variance or of white noise type). Moreover, we analyse the discrepancy principle as an adaptive stopping rule for a stochastic gradient descent, as a non-Filter based computationally efficient regularisation method.

Talk: "Sensitivity analysis for identification of voids under Navier's boundary conditions in linear elasticity"

We kindly invite you to the talk "Sensitivity analysis for identification of voids under Navier's boundary conditions in linear elasticity" by Bochra Mejri. Wednesday, Jan. 27th, 15:00 Vienna Time.

Online at:

This talk is concerned with a geometric inverse problem related to the two-dimensional linear elasticity system. Thereby, voids under Navier’s boundary conditions are reconstructed from the knowledge of partially over-determined boundary data. The proposed approach is based on the so-called energy-like error functional combined with the topological sensitivity method. The topological derivative of the energy-like misfit functional is computed through the topological-shape sensitivity method. Firstly, the shape derivative of the corresponding misfit function is presented. Then, an explicit solution of the fundamental boundary-value problem in the infinite plane with a circular hole is calculated by the Muskhelishvili formulae. Finally, the asymptotic expansion of the topological gradient is derived explicitly with respect to the nucleation of a void. Numerical tests are performed in order to point out the efficiency of the developed approach.

Talk: "Multi-scale classification for electro-sensing"

We kindly invite you to the talk "Mathematics of Biomimetics for Active Electro-sensing" by Andrea Scapin. Wednesday, Jan. 13th, 15:00 Vienna Time.

Online at:

The biological behavior of weakly electric fish has been studied by scholars for years. These fish orient themselves at night in complete darkness by using electrosensory information, which makes these animals an ideal subject for developing bio-inspired imaging techniques. Such interest has motivated a huge number of studies addressing the active electro-sensing problem from many different perspectives since Lissmann and Machin’s work. One of the most noteworthy potential bio-inspired applications is in underwater robotics. Building autonomous robots with electro-sensing technology may supply unexplored navigation, imaging and classification capabilities, especially when the sight is unreliable due, for example, to the turbidity of the surrounding waters or the poor lighting conditions.

In this talk we present a premier and innovative (real-time) multi-scale method for target classification in electro-sensing. The intent is that of mimicking the behavior of the weakly electric fish, which is able to retrieve much more information about the target by approaching it. The method is based on a family of transform-invariant shape descriptors computed from generalized polarization tensors (GPTs) reconstructed at multiple scales. The evidence provided by the different descriptors at each scale is fused using Dempster-Shafer Theory.

Dissertation of Christopher Hofmann
Congratulations to Christopher Hofmann – working within within the SCIP project – for successfully defended his dissertation "Contributions to regularization theory and practice of certain nonlinear inverse problems"!
Current Open Position (pre-doc)

We're currently offering a PhD position within the framework of Vienna School of Mathematics on the topic of Optimal Control of Waves in Dead Water. (→ detailed information)

Handbook of Mathematical Methods in Imaging, Chapter Downloads

We are proud to report that since the online publication of the Handbook of Mathematical Methods in Imaging (Second Edition) in 2015 there have been a total of 175366 chapter downloads!

Cancer diagnosis with mathematics

Otmar Scherzer presented at the Research Newsletter (July/August 2020) of the University of Vienna how mathematics can be used to improve cancer diagnosis. This work is part of the SFB research project Tomography Across the Scales. The considered methods have applications from astrophysics to molecular biology.

The main idea (also called inverse problem) is to use tomographic measurements of a biological tissue in order to recover its properties (distinguish between healthy and diseased parts) without damaging it. The created algorithms are tested with simulated and experimental data and the results are promising.

The full article (in German).

Otmar Scherzer, new Editor-in-Chief of the Journal Inverse Problems
Otmar Scherzer is the new Editor-in-Chief of the journal Inverse Problems. He is replacing Professor Simon Arridge (University College London), who has been in this position since 2015. Otmar Scherzer was a member of the Editorial Board of Inverse Problems for a long time, he has acted as Guest Editor on several special issues and he has also published many of his works in this journal.
Studyly: App to motivate more young people to study maths
Our master student Leon Frischauf has started the e-learning platform Studyly, encouraging students from all over Austria to study maths online. Currently Studyly has been used by over 11 000 students for the preparation for the Matura (Austrian final exams) with the goal to increase young peoples interest in mathematics. See also the newspaper article in the "Kurier" (in German).
Dissertation of Melanie Melching
Congratulations to Melanie Melching, who successfully defended her dissertation "Regularization with integral representations of Sobolev norms of manifold-valued functions"!
Online seminar RICAM - Fudan
We're inviting you to join the "Online seminar RICAM - Fudan" on June, 10th with Shuai Lu as speaker – "When randomness meets inverse problems" – and Andrea Aspri – "Data driven regularization by projection". Start is 14:00 in Vienna Time.
Dissertation of Alexander Beigl
Congratulations to Alexander Beigl, who successfully defended his dissertation "An Optimal Control Approach to Photoacoustic Tomography and a New Approach for Quantitative Reconstruction"!
Peter Elbau Receives the EAIP Young Scientist Award

Every two years the Eurasian Association on Inverse Problems (EAIP) awards scientists under the age of fourty for particular merits in inverse problems analysis and its applications.

We are proud to announce Peter Elbau has been selected with Joonas Ilmavirta to receive this award in 2020!

Winter school "Applied mathematics: as useful as exciting"

Last week (02.03 – 06.03) took place in Kefermarkt the first winter school of the Austrian Study Foundation (Österreichische Studienstiftung). That was the fourth seminar organized by the Austrian Academy of Sciences (Österreichische Akademie der Wissenschaften) with the title “Applied mathematics: as useful as exciting”.

Selected pupils from schools around Austria had the opportunity to learn and develop themselves applications of mathematics in everyday life. The four topics where: Financial mathematics, mathematical methods in Tomography, graph theory and mathematical modeling of sound.

Axel Kittenberger and Leonidas Mindrinos, from our group, presented the fundamentals of the Radon transform, its properties and application to tomography. The students had the opportunity to make 3D origami objects, image them with a system imitating an optical tomographic setup and then obtain the reconstructed pictures.

–> click here for an online raytracer of a volumetric reconstruction

Front cover picture in "Inverse Problems"
A figure from the research paper "Preconditioning Inverse Problems for Hyperbolic Equations with Applications to Photoacoustic Tomography" by Alexander Beigl, Otmar Scherzer, Jarle Sogn (JKU, Linz) and Walter Zulehner (JKU, Linz) got chosen for the front cover of the International Journal "Inverse Problems". The picture appearing at the Volume 36, Number 1 of the journal presents initial source reconstructions from Photoacoustic Tomography data.
Otmar Scherzer in ECMI Annual Report
Otmar Scherzer gave an interview to the ECMI Annual Report 2018: “Mathematics with industry: driving innovation”. He describes how the field of industrial mathematics evolved over the last years and his recent research projects, focusing on the SFB project “Tomography across the scales”. The Report is edited by A. Münch (University of Oxford) and the interview was conducted by L. Mindrinos (RICAM, Linz). You can read the whole report here.

Florian Faucher posted on ECMI blog
Our group is part of the European Consortium for Mathematics in Industry (ECMI). Florian posted an article related to his project funded by the Austrian Science Fund FWF, under the Lise Meitner fellowship grant number M2791-N.
Denise Schmutz posted on ECMI blog
Our group is part of the European Consortium for Mathematics in Industry (ECMI). This week, Denise posted an article related to her work under the SFB project "Tomography Across the scales".
Article in Krone newspaper "Laserblitz und Donner" by O. Scherzer

Otmar Scherzer presented in "Kronenzeitung" within the weekly column "Krone der Wissenschaft" the ideas and the scopes of the SFB project "Tomography Across the Scales". The article (in german) addresses the general principles of tomography (computed and photoacoustic). The article can be acquired on PressReader.

SFB goes to Banff, Canada

Otmar Scherzer was a member of the organizing committee of the “Reconstruction Methods for Inverse Problems” workshop in Banff, Canada, June 23-28, 2019. This workshop brought together researchers working on inverse problems coming from medical imaging, non destructive testing, computer vision and geophysics. The PI of sub-project “Quantitative Coupled Physics Imaging”, Peter Elbau and the post-doctoral researcher of the sub-project “Tomography with Uncertainties”, Ekaterina Sherina presented their recent work related to our SFB project “Tomography Across the Scales”.

Photo credit: The Banff International Research Station
Saving lives with mathematics

“Die Presse” printed an an interview with Otmar Scherzer on combining PAT and OCT to detect tumors. (“innovationorigins” published an english version of similar content).

This research is being done within the SFB Tomography Across the Scales.
Making cancer visible early
PhD position in the project "Novel Error Measures and Source Conditions of Regularization Methods"

We are offering a Doctorate Research Position within the FWF-funded International Project Novel Error Measure and Source Conditions of Regularization Methods.

detailed description.

PhD position in the project "Weighted X-ray transform and applications"

RICAM, Linz, is offering a PhD Student position in the field of Inverse Problems / Tomography.

detailed description

Vienna Night Run

The CSC team participiated at the Vienna Night Run. Despite a sudden cold snap everyone finished!

Reconstruction Methods for Inverse Problems (19w5092)

at Banff, Alberta from Sunday, June 23 to Friday June 28, 2019


  • Elena Beretta (NYU Abu Dhabi & Politecnico di Milano)
  • Uri Ascher (University of British Columbia)
  • Otmar Scherzer (University of Vienna)
  • Luminita Vese (University of California, Los Angeles)


Inverse problems require to determine the cause from a set of indirect observations. Such problems appear in medical imaging, non destructive testing of materials, computerized tomography, source reconstructions in acoustics, computer vision and geophysics, to mention but a few. The 21st century is the golden age of computer imaging: Measurement devices have become enormously powerful and huge amounts of data are recorded at every eye glimpse. Moreover, computer technology has developed to such a high degree of efficiency that the evaluation of such an enormous amount of data has become possible *if* adequate mathematical and computational tools are used.

Recently, the community has been exposed to fundamentally new mathematical models (such as learning), which stimulated exciting theoretical developments and new computational algorithms for solving complicated large scale inverse problems. This workshop will survey modern and identify new mathematical and computational developments for tackling such problems.

more details
Quasilinear Equations, Inverse Problems and their Applications
The fourth international conference "Quasilinear Equations, Inverse Problems and their Applications" will take place in Dolgoprudny, Russia, December 3-5, 2018. We are inviting talk submissions until September 15th.
Otmar Scherzer receives the 2018 EAIP award

The Eurasian Association on Inverse Problems (EAIP) is a non-governmental organization working to ensure a coordination between inverse problems research groups and scientific schools in Eurasian countries, by providing international conferences, meetings and summer schools on inverse problems, both in theory and applications.

The association has established an "EAIP Award" to recognize outstanding scientific contributions to the field of inverse problems and continuous efforts to foster cooperation between researchers of Eurasian countries.

SFB “Tomography Across the Scales” presented in uni:view

The SFB “Tomography Across the Scales” with Otmar Scherzer (SFB speaker and subproject leader) and Computational Science Center member Peter Elbau (subproject leader) is presented in the university magazine uni:view (german).

Inverse Problems in the ALPS II and Inaugural Meeting of the SFB "Tomography Across the Scales"

The Radon Institute for Computational and Applied Mathematics in Linz, the Doctoral Program “Computational Mathematics” and the SFB “Tomography across the Scales” are organizing the international workshop Inverse Problems in the ALPS II and Inaugural Meeting of the SFB “Tomography across the Scales” at the Obergurgl University Center.

The SFB Inaugural Meeting starts on March, 18th after dinner and ends on March, 20th, 2018. The workshop “Inverse Problems in the Alps II” (successor of the workshop “Inverse Problems in the Alps” held in March 2016) starts on March, 21st and ends on March, 23rd 2018 after lunch.

more information
Master's Thesis of Denise Schmutz
We congratulate Denise Schmutz for successfully defending her master's thesis "Reconstruction of Projection Orientations in Cryo-Electron Microscopy" supervised by Otmar Scherzer!
Dissertation of Cong Shi
Congratulations to Cong Shi, who successfully defended her dissertation "High-Resolution Imaging for Photoacoustic Tomography and Optical Coherence Tomography"!
CSC on ECMI blog
Our group is part of the European Consortium for Mathematics in Industry (ECMI). This week, you can find our students project here.
Habilitation of Peter Elbau
We congratulate Peter Elbau on successfully defending is habilitation thesis – "A Struggle for Quantitative Imaging. From Photoacoustic and Optical Coherence Tomography to Regularisation Theory" – on June 26th!
Mathematics for "inner values"
Otmar Scherzer gave an Interview about the Radon Transformation published by the ÖAW.
Dissertation of Guozhi Dong
Congratulations to Guozhi Dong, who successfully defended his dissertation "Regularization and Imaging Methods for Solving Inverse Problems with Solutions on Surfaces" on Mar 24th!
Radon Transformation and Origami Birds
The "Standard" published a video interview "Radon-Transformation: Was ein Origami-Vogel mit Mathematik zu tun hat" of Otmar Scherzer explaining the working principle of tomography on a vivid experiment which produces from the recorded shadows of a rotating, transparent origami figure in front of an overhead projector a three-dimensional computer model.
Mini Special Semester "100 Years of the Radon Transform"
The Mini Special Semester "100 Years of the Radon Transform" takes place in Linz, March 27 - July 14, 2017 and consists of the two events:
  • Conference "100 Years of the Radon Transform" - March 27 - 31, 2017
  • Summer School & Workshop "Quantitative Tomographic Imaging – Radon meets Bell and Maxwell" — July 10—14, 2017
Teaching Award for Peter Elbau
CSC member Peter Elbau received the faculty Mathematics award for outstanding merits in the field of teaching.
Dissertation of Aniello Raffaele Patrone
Congratulations to Aniello Raffaele Patrone, who successfully defended his dissertation "Variational Models of Visual Attention with a Special Focus on Dynamic Sequences" on Sep 12th!
Leonidas Mindrinos posted on ECMI blog
Our group is part of the European Consortium for Mathematics in Industry (ECMI). This week, Leonidas Mindrinos posted an article.
Lukas Lang posted on ECMI blog
Our group is part of the European Consortium for Mathematics in Industry (ECMI). This week, Lukas Lang posted an article.
Dissertation of Thomas Glatz
Congratulations to Thomal Glatz, who successfully defended his dissertation +"Photoacoustic Inversion Based on In-depth Wave Models" on Apr 7th!
CSC in Inverse Problems Highlights of 2015
An article by Thomas Widlak and Otmar Scherzer has been selected as highlight of 2015.
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Computational Science Center
Faculty of Mathematics
University of Vienna

Oskar-Morgenstern-Platz 1
1090 Wien
T: +43-1-4277-55771