As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question (Antun et al., 2020; Gottschling et al., 2020). However, recent work has shown that, compared to total variation (TV) minimization, when appropriately regularized, DNNs show similar robustness to adversarial noise in terms of $\ell^2$-reconstruction error (Genzel et al., 2022). We consider a different notion of robustness, using the $\ell^\infty$-norm, and argue that localized reconstruction artifacts are a more relevant defect than the $\ell^2$-error. We create adversarial perturbations to undersampled magnetic resonance imaging measurements (in the frequency domain) which induce severe localized artifacts in the TV-regularized reconstruction. Notably, the same attack method is not as effective against DNN based reconstruction. Finally, we show that this phenomenon is inherent to reconstruction methods for which exact recovery can be guaranteed, as with compressed sensing reconstructions with $\ell^1$- or TV-minimization.

翻译：随着深度学习神经网络在图像重建任务中的应用日益广泛，其可靠性受到质疑（Antun等，2020；Gottschling等，2020）。然而，近期研究表明，与全变分最小化相比，当适当正则化时，深度神经网络在$\ell^2$重建误差方面表现出相似的对抗噪声鲁棒性（Genzel等，2022）。本文采用基于$\ell^\infty$范数的不同鲁棒性定义，论证局部化重建伪影比$\ell^2$误差更具实际危害性。我们针对欠采样磁共振成像测量数据（频域）生成对抗扰动，这些扰动会在全变分正则化重建中引发严重的局部化伪影。值得注意的是，同样的攻击方法对基于深度神经网络的重建效果不佳。最后，我们证明该现象本质上是具有精确恢复保证的重建方法（如采用$\ell^1$或全变分最小化的压缩感知重建）所固有的特性。