  Deep neural networks give state-of-the-art performance for inverse problems
such as reconstructing images from few and noisy measurements, a problem
arising in accelerated magnetic resonance imaging (MRI). However, recent works
have raised concerns that deep-learning-based image reconstruction methods are
sensitive to perturbations and are less robust than traditional methods: Neural
networks (i) may be sensitive to small, yet adversarially-selected
perturbations, (ii) may perform poorly under distribution shifts, and (iii) may
fail to recover small but important features in the image. In order to
understand whether neural networks are sensitive to such perturbations, in this
work, we measure the robustness of different approaches for image
reconstruction including trained neural networks, un-trained networks, and
traditional sparsity-based methods. We find, contrary to prior works, that both
trained and un-trained methods are vulnerable to adversarial perturbations.
Moreover, we find that both trained and un-trained methods tuned for a
particular dataset suffer very similarly from distribution shifts. Finally, we
demonstrate that an image reconstruction method that achieves higher
reconstruction accuracy, also performs better in terms of accurately recovering
fine details. Thus, the current state-of-the-art deep-learning-based image
reconstruction methods enable a performance gain over traditional methods
without compromising robustness.
