  MRI reconstruction techniques based on deep learning have led to
unprecedented reconstruction quality especially in highly accelerated settings.
However, deep learning techniques are also known to fail unexpectedly and
hallucinate structures. This is particularly problematic if reconstructions are
directly used for downstream tasks such as real-time treatment guidance or
automated extraction of clinical paramters (e.g. via segmentation).
Well-calibrated uncertainty quantification will be a key ingredient for safe
use of this technology in clinical practice. In this paper we propose a novel
probabilistic reconstruction technique (PHiRec) building on the idea of
conditional hierarchical variational autoencoders. We demonstrate that our
proposed method produces high-quality reconstructions as well as uncertainty
quantification that is substantially better calibrated than several strong
baselines. We furthermore demonstrate how uncertainties arising in the MR
econstruction can be propagated to a downstream segmentation task, and show
that PHiRec also allows well-calibrated estimation of segmentation
uncertainties that originated in the MR reconstruction process.
