Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes

B Harrach - Inverse problems, 2019 - iopscience.iop.org
For the linearized reconstruction problem in electrical impedance tomography with the
complete electrode model, Lechleiter and Rieder (2008 Inverse Problems 24 065009) have …

Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability

B Harrach, YH Lin - SIAM Journal on Mathematical Analysis, 2020 - SIAM
In this work, we use monotonicity-based methods for the fractional Schrödinger equation
with general potentials q in L^ ∞ (Omega) in a Lipschitz bounded open set Omega ⊂ R^ n …

Calderón's inverse problem with a finite number of measurements

GS Alberti, M Santacesaria - Forum of mathematics, sigma, 2019 - cambridge.org
We prove that an L∞ potential in the Schrödinger equation in three and higher dimensions
can be uniquely determined from a finite number of boundary measurements, provided it …

Continuous generative neural networks

GS Alberti, M Santacesaria, S Sciutto - arXiv preprint arXiv:2205.14627, 2022 - arxiv.org
In this work, we present and study Continuous Generative Neural Networks (CGNNs),
namely, generative models in the continuous setting: the output of a CGNN belongs to an …

Infinite-dimensional inverse problems with finite measurements

GS Alberti, M Santacesaria - Archive for Rational Mechanics and Analysis, 2022 - Springer
We present a general framework to study uniqueness, stability and reconstruction for infinite-
dimensional inverse problems when only a finite-dimensional approximation of the …

Inverse problems on low-dimensional manifolds

GS Alberti, Á Arroyo, M Santacesaria - Nonlinearity, 2022 - iopscience.iop.org
We consider abstract inverse problems between infinite-dimensional Banach spaces. These
inverse problems are typically nonlinear and ill-posed, making the inversion with limited and …

Global uniqueness and Lipschitz-stability for the inverse Robin transmission problem

B Harrach, H Meftahi - SIAM Journal on Applied Mathematics, 2019 - SIAM
In this paper, we consider the inverse problem of detecting a corrosion coefficient between
two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse …

Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion

YF Albuquerque, A Laurain, I Yousept - SIAM Journal on Applied Mathematics, 2021 - SIAM
Velocity models presenting sharp interfaces are highly relevant in seismic imaging, eg, for
imaging the subsurface of the Earth in the presence of salt bodies. In order to mitigate the …

Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem

B Harrach - Numerische Mathematik, 2021 - Springer
We derive a simple criterion that ensures uniqueness, Lipschitz stability and global
convergence of Newton's method for the finite dimensional zero-finding problem of a …

[HTML][HTML] Inverse problem for the Rayleigh system with spectral data

MV de Hoop, A Iantchenko - Journal of Mathematical Physics, 2022 - pubs.aip.org
We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat
elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction …