that appear the same in difference images, such as pneumothorax versus hyperinflation or atelectasis versus pulmonary edema, and for the classification of a breast lesion as a cyst or tumor, benign or malignant. [[For thoracic imaging, 2D images are particularly relevant for ARDS patients, for which a single cross-sectional image well represents the heterogeneous mechanical properties of dependent and non-dependent lung regions \[[@ElDash2016]\].]{}]{} However, due to the sensitivity of the severely ill-posed inverse conductivity problems to modeling errors such as errors in electrode locations, contact impedance, and domain shape, absolute images with good spatial resolution and few artefacts are notoriously difficult to compute. Minimization-based methods, such as Gauss-Newton approaches require an accurate forward model that can predict the voltages on the electrodes from a candidate conductivity distribution with high precision. A typical forward model computed with the finite element method (FEM) requires precise knowledge of boundary shape and electrode positions, as well as a very high number of elements to achieve accuracy, and so solving the forward problem at each iteration in the Gauss-Newton method has high computational cost. When real-time imaging is desirable, such as in pulmonary applications, this computational burden and imprecise boundary knowledge pose significant challenges.

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