Robust MRI Reconstruction by Smoothed Unrolling (SMUG)

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 or random 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 these 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 noise, 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 DL-based MRI reconstruction models. We theoretically analyze the robustness of our method in the presence of perturbations. Compared to vanilla RS and other recent approaches, 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. Our code is available at https://github.com/sjames40/SMUG_journal.