  As the popularity of deep learning (DL) in the field of magnetic resonance
imaging (MRI) continues to rise, recent research has indicated that DL-based
MRI reconstruction models might be excessively sensitive to minor input
disturbances, including worst-case additive perturbations. This sensitivity
often leads to unstable, aliased images. This raises the question of how to
devise DL techniques for MRI reconstruction that can be robust to train-test
variations. 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 approach. RS, which improves the tolerance of a
model against input noises, has been widely used in the design of adversarial
defense approaches for image classification tasks. Yet, we find that the
conventional design that applies RS to the entire DL-based MRI model is
ineffective. In this paper, we show that SMUG and its variants address the
above issue by customizing the RS process based on the unrolling architecture
of a DL-based MRI reconstruction model. Compared to the vanilla RS approach, we
show that SMUG improves the robustness of MRI reconstruction with respect to a
diverse set of instability sources, including worst-case and random noise
perturbations to input measurements, varying measurement sampling rates, and
different numbers of unrolling steps. Furthermore, we theoretically analyze the
robustness of our method in the presence of perturbations.
