Deep Generative Physical Models for MRI Reconstruction

Recently, deep learning techniques have been used as powerful
data-driven reconstruction methods for inverse problems, and in
particular have led to reduced scan times in magnetic resonance
imaging (MRI). Typically, these methods are implemented using
end-to-end supervised learning based on idealized imaging conditions.
While promising, reconstruction quality is known to degrade when
applied to natural measurement and anatomy perturbations. In this talk
we present an alternative approach to deep learning reconstruction
based on distribution learning, in which we train a deep generative
model to learn image priors without reference to the measurement
process. We show that decoupling the measurement and statistical
models provides a powerful framework for MRI reconstruction. We
leverage recent advances in score-based generative modeling to learn
the prior distribution and we pose the image reconstruction task as
posterior sampling. We show that this approach is competitive with
end-to-end methods when applied to in-distribution data, and we
demonstrate theoretical and empirical robustness to various
out-of-distribution shifts. In cases where the distribution shift is
large, we empirically show a small amount of training data is
sufficient to recover the performance. Finally, we demonstrate the
utility of our framework for image reconstruction in the presence of
subject motion.