Inverse Problems and Optimization

Abstract: 

Inverse problems concern the reconstruction of unknown quantities from direct or indirect observations, and they play a central role in many areas of mathematics and applicational fields such as medical imaging, nondestructive testing or geophysical exploration. This mini-symposium brings together recent developments across several key topics, including scattering theory, optimization methods, and electrical impedance tomography. In addition to practical and computational approaches, fundamental theoretical aspects of inverse problems will also be addressed. The session features contributions primarily from early-career researchers, including PhD students and postdoctoral fellows, highlighting fresh perspectives and emerging work in the field.

Confirmed Speakers:

Speaker: Suvi Anttila (University of Oulu)
Title: TBA
Abstract: TBA

Speaker: Khaoula El Maddah (University of Oulu)
Title: TBA
Abstract: TBA

Speaker: Spyridon Filippas (University of Helsinki)
Title: TBA
Abstract: TBA

Speaker: Aada Hakula (Aalto University)
Title: TBA
Abstract: TBA

Speaker: Allti Jääskeläinen (Aalto University)
Title: TBA
Abstract: TBA

Speaker: Roland Griesmaier, Marvin Knöller, Eliane Ariadne Felicitas Kummer (Karlsruhe Institute of Technology)
Title: Domain derivative and shape reconstruction for a transient inverse backscattering problem
Abstract: We are interested in the shape reconstruction of a three-dimensional penetrable scattering obstacle from backscattering measurements of the associated time-dependent far field.
To this avail, we study the temporal domain derivative (TDD) for a time-dependent acoustic scattering problem, namely the transmission problem for the wave-equation. We can then employ this domain derivative in an iterative reconstruction algorithm similar to the TDD for sound-soft scattering objects and near field measurements for a single incident wave, as has been studied in Knöller and Nick, Numer. Math. 158(1), 2026.
For this, we first consider the operator, which maps the boundary of the penetrable scattering object to the far field, measured at a backscattering point \(-d \in \mathbb{S^2}\) at time \(t \in \mathbb{R}\).
The TDD is then given by the point-evaluation of the Fréchet derivative of this operator with respect to perturbations of the boundary.
To obtain the existence of the domain derivative in the time domain, we first study the corresponding problem in the Laplace domain.
By establishing frequency bounds for the domain derivative in the frequency domain and by utilizing Paley-Wiener's theorem we prove the existence of the TDD in the time domain. By applying Runge-Kutta convolution quadrature as well as a regularized Gauß-Newton algorithm, we employ the time-discrete temporal domain derivative to describe an algorithm to reconstruct the boundary of a three-dimensional penetrable scattering object from time domain back-scattering measurements of the far field.
We demonstrate the efficiency of our algorithm by presenting numerical simulations.

Speaker: Teresa Rauscher (University of Graz)
Title: TBA
Abstract: TBA

Speaker: Hjørdis Schlüter (University of Helsinki)
Title: TBA
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Speaker: Vigdis Toresen (Aalto University)
Title: TBA
Abstract: TBA