# Mission Statement

The core research topics of the Computational Science Center are Inverse Problems and Image Analysis. The common thread among these areas is a canonical problem of recovery of an object (function or image) from partial or indirect information. Particular research topics are:

- Geometrical Modeling for Image Analysis.
- Mathematical Modeling and numerical simulations in Coupled Physics Imaging.
- Variational regularization methods for Image Analysis and Inverse Problems.
- Mathematical models for visual attention.

# News

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: https://meet.csc.univie.ac.at/b/axe-7hr-2ad

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.

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: https://meet.csc.univie.ac.at/b/axe-phh-y2a

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.

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: https://meet.csc.univie.ac.at/b/axe-zjv-dya

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.

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)

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!

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.