  Although deep learning (DL) has gained much popularity for accelerated
magnetic resonance imaging (MRI), recent studies have shown that DL-based MRI
reconstruction models could be oversensitive to tiny input perturbations (that
are called 'adversarial perturbations'), which cause unstable, low-quality
reconstructed images. This raises the question of how to design robust DL
methods for MRI reconstruction. To address this problem, we propose a novel
image reconstruction framework, termed SMOOTHED UNROLLING (SMUG), which
advances a deep unrolling-based MRI reconstruction model using a randomized
smoothing (RS)-based robust learning operation. RS, which improves the
tolerance of a model against input noises, has been widely used in the design
of adversarial defense for image classification. Yet, we find that the
conventional design that applies RS to the entire DL process is ineffective for
MRI reconstruction. We show that SMUG addresses the above issue by customizing
the RS operation based on the unrolling architecture of the DL-based MRI
reconstruction model. Compared to the vanilla RS approach and several variants
of SMUG, we show that SMUG improves the robustness of MRI reconstruction with
respect to a diverse set of perturbation sources, including perturbations to
the input measurements, different measurement sampling rates, and different
unrolling steps. Code for SMUG will be available at
https://github.com/LGM70/SMUG.
