275 citations · 957 across the 58 of their papers we have counts for
8 papers · 1 filter
Convolutional neural networks in phase space and inverse problems
Gunther Uhlmann, Yiran Wang
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of pr…
Inverting the local geodesic ray transform of higher rank tensors
Maarten V. de Hoop, Gunther Uhlmann, Jian Zhai
Consider a Riemannian manifold in dimension with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tens…
Inverse Problem for Fractional-Laplacian with Lower Order Non-local Perturbations
Sombuddha Bhattacharyya, Tuhin Ghosh, Gunther Uhlmann
In this article, we study a model problem featuring a Lévy process in a domain with semi-transparent boundary by considering the following perturbed fractional Laplacian operator \…
Inverse problems for the stationary transport equation in the diffusion scaling
Ru-Yu Lai, Qin Li, Gunther Uhlmann
We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusiv…
The Calderón problem for quasilinear elliptic equations
Claudio Muñoz, Gunther Uhlmann
In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential it…
Determination of space-time structures from gravitational perturbations
Gunther Uhlmann, Yiran Wang
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gr…