# 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 are happy to announce that the educational paper Computed Origami Tomography by Axel Kittenberger, Leonidas Mindrinos and Otmar Scherzer got published in SIAM Review.

The authors demonstrate the principles of computer tomography using harmless light instead of x-rays. With the provided instructions, building your own DIY-tomograph at home is very much possible. See for 3D reconstructions of an origami crane as exemplary result.

We kindly invite you to the talk "Concentration inequalities for cross-validatin in scattered data approximation" by Felix Bartel, Apr. 14th, 14:00pm Vienna Time.

Join Zoom Meeting: https://oeaw-ac-at.zoom.us/j/92440653189?pwd=cm1KVCtSaHViTXNjYkxuYVpNVU9qUT09

Meeting-ID: 924 4065 3189

Password: fY9hzA

We present a new factorization method for recovering a conductivity inclusion in two dimensions from multi-static measurements. A conductivity inclusion induces a perturbation in the background potential, and the perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). We derive a factorization formula for the matrix composed of the GPTs in terms of the material parameters and the coefficients of the exterior conformal mapping associated with the inclusion. Using this formula, we induce accurate representations for the coefficients of the conformal mapping in terms of the GPTs. Our approach provides a non-iterative method for recovering the shape of a Lipschitz inclusion with arbitrary finite conductivity.

We are offering a Post Doc Research/Coordination Position within on Special Research Programmes (SFB F68) Tomography Across the Scales at the Faculty of Mathematics, University of Vienna, funded by the Austrian Science Fund (FWF) (https://www.fwf.ac.at/de/). The position is full time, 40 hours per week, for an initial period of two year with a possible extension till 28. February 2026.

We kindly invite you to the talk "Adaptive spectral decomposition for inverse medium problems" by Marcus J. Grote, March 30, 2:00pm Vienna Time.

This is part of the Joint Fudan - RICAM Seminar on Inverse Problems

The meeting is a hybrid meeting, come either in person to the meeting room 9 at Oskar-Morgenstern-Platz 1, 9th floor or

join the zoom meeting: https://zoom.us/join Meeting-ID: 694 9293 2905 Password: SCMS

*Abstract:*
Inverse medium problems involve the reconstruction of a spatially varying
unknown medium from available observations of a scattered wave field.
Typically, they are formulated as PDE-constrained optimization problems
and solved by an inexact Newton-like iteration.
Clearly, standard grid-based representations are very general
but often too expensive due to the resulting high-dimensional
search space. Adaptive spectral inversion (ASI) instead expands the
unknown medium in a basis of eigenfunctions of a judicious elliptic operator,
which depends itself on the current iterate. Thus, instead of a grid-based
discrete representation combined with standard Tikhonov regularization,
the unknown medium is projected to a small finite-dimensional subspace,
which is iteratively adapted using dynamic thresholding.
Rigorous error estimates of the adaptive spectral decomposition (ASD)
are proved for an arbitrary piecewise constant medium.

Within the FWF-funded International Project New Inverse Problems in Superresolution Microscopy, we offer a Doctorate Research Position (2 years with a possible extension of up to 4 years) at the Faculty of Mathematics, University of Vienna The position is available from July 1st, 2022. The duties concern research in inverse problems related to superresolution microscopy, regularization methods and mathematical modeling. Publications in high quality journals, networking with partners in applied sciences is desired. The salary is as suggested by the FWF according to a doctorate position. The working load for the project is 30 hours per week.

(→ detailed information)We kindly invite you to the talk "Control problem of a water waves system in a tank" by Pei, Su, Apr. 6th, 3:00pm Vienna Time.

Contact to get an invite link.

We first study the stability of a class of skew-adjoint control systems.
With the assumptions on the spectrum of the evolution operators involved
in the control system, we obtain an explicit non-uniform decay rate of the
energy, provided that the initial data is smooth.

Then we consider a small-amplitude water waves system in a rectangular
domain, where the control acts on one lateral boundary, by imposing the
velocity of the water. The equation is a fully linear and fully dispersive
version of the Zakharov-Craig-Sulem formulation. Based on the Dirichlet to
Neumann and Neumann to Neumann maps, we establish the well-posedness
of the whole system, which is addressed by formulating the equations as an
abstract linear control system. Afterwards, there exists a feedback functional,
such that the corresponding control system is strongly stable. We obtain the
decay rate of the energy by using the above general results.

Finally, we consider the asymptotic behaviour of the above system in
the shallow water regime, i.e. the horizontal scale of the domain is much
larger than the typical water depth. We prove that the solution of the water
waves system converges to the solution of the one dimensional wave equation
with Neumann boundary control, when taking the shallowness limit. Our
approach is based on a detailed analysis of the Fourier series and the di-
mensionless version of the evolution operators mentioned above, as well as a
scattering semigroup and the Trotter-Kato approximation theorem.

This is partially collaborated with M. Tucsnak (Bordeaux) and G. Weiss
(Tel Aviv).

We kindly invite you to the talk "Matrix factorization for the multi-static data and its application to shape recovery of a planar inclusion." by 최두성 Choi, Doosung, Apr. 6th, 1:00pm Vienna Time.

Contact to get an invite link.

We present a new factorization method for recovering a conductivity inclusion in two dimensions from multi-static measurements. A conductivity inclusion induces a perturbation in the background potential, and the perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). We derive a factorization formula for the matrix composed of the GPTs in terms of the material parameters and the coefficients of the exterior conformal mapping associated with the inclusion. Using this formula, we induce accurate representations for the coefficients of the conformal mapping in terms of the GPTs. Our approach provides a non-iterative method for recovering the shape of a Lipschitz inclusion with arbitrary finite conductivity.