| Abstract: |
| We aim to derive globally convergent reconstruction algorithms for the inverse coefficient problem of Electrical Impedance Tomography (aka the famous Calder\`on problem) and its application in lung imaging. Our main tool is to reformulate the problem as a concave semidefinite minimization problem. This allows to construct a globally convergent EIT reconstruction algorithm that is computationally feasible for a moderately low number of unknowns.
We then combine this approach with the recent data-driven observation that realistic lung images lie on a nonlinear manifold that is much lower dimensional than the space of all possible images. Variational autoencoder techniques can be used to learn such a low-dimensional parametrization, but a standard out-of-the-box autoencoder would destroy the concavity properties of the reconstruction problem. Hence, we show how to adjust the autoencoder training process in such a way that concavity (and thus global convergence of the final reconstruction strategy) is preserved. |
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