The reconstruction of high-fidelity resolution brain MR images is especially challenging because of the highly complex brain structure. Most promising approaches for this task are autoencoders and generative models such as Variational Autoencoders (VAE) or Generative Adversarial Networks (GAN). In Unsupervised Anomaly Detection (UAD), these architectures are only trained with images of healthy brain anatomy and not with images containing anomalies such as lesions. Therefore, processing an anomalous input image $\pmb{x}$ with an architecture trained to reconstruct healthy MR images should produce a high reconstruction error $r$ indicating that the input MR image is likely to exhibit anomalies.

So far developed models for this task are either limited to low resolution reconstructions so that quite a lot of information is lost or to only small image regions. Baur et al. hypothesize that these restrictions are caused by the low dimensionality of the latent space of the models even though a high capacity would be necessary to reconstruct highly complex brain MR images. Thus, Baur et al. introduce skip connections in the autoencoder to enable detailed high resolution reconstructions due to the enhanced gradient flow. In addition, the application of dropout on the skip connections shall prevent the model from learning the identity of the input image since only the corresponding healthy anatomy of the possibly anomalous input image shall be reconstructed. Sampling the networks parameter $\pmb{\theta}$ from a Bernoulli distribution $\pmb{\theta} \sim \mathcal{B}(p)$ with $p$ being the dropout rate  also turns the Skip-Autoencoder into a Bayesian neural network by using a Monte Carlo dropout at test time.
The proposed Skip Autoencoder and the Bayesian Skip-Autoencoder are tested on Mutiple Sclerosis and Glioblastoma datasets and evaluated using the Precision-Recall-Curve (PRC), the AUPRC, and the Dice Score. An investigation of the Bernoulli dropout yields that no input identity is learnt independent on the dropout. A random weight initialization seems to be sufficient. Considering the skip-connections, the best performance is achieved by a single skip-connection close to the bottleneck layer. Applying more skip connections improves the performance on the Glioblastoma test set but reduces the performance on the Multiple Sclerosis test set.

In general, the non-Bayesian Skip-Autoencoder exceeds the performance of the Bayesian Skip-Autoencoder because in the calculation of the reconstruction residual $r = \rvert \pmb{x} - \pmb{\hat{x}} \rvert$ for the Bayesian Skip-Autoencoder the predictive mean of $n$ Monte Carlo samples is applied as reconstructed image $\pmb{\hat{x}}$ which causes a blurriness in the reconstructions  $\pmb{\hat{x}}$. However, the Bayesian Skip-Autoencoder enables to quantify the epistemic uncertainty because the pixels of hyperintense anomalies have a low variance compared to normal tissue.