Untrained neural networks pioneered by Deep Image Prior (DIP) have recently enabled MRI reconstruction without requiring fully-sampled measurements for training. Their success is widely attributed to the implicit regularization induced by suitable network architectures. However, the lack of understanding of such architectural priors results in superfluous design choices and sub-optimal outcomes. This work aims to simplify the architectural design decisions for DIP-MRI to facilitate its practical deployment. We observe that certain architectural components are more prone to causing overfitting regardless of the number of parameters, incurring severe reconstruction artifacts by hindering accurate extrapolation on the un-acquired measurements. We interpret this phenomenon from a frequency perspective and find that the architectural characteristics favoring low frequencies, i.e., deep and narrow with unlearnt upsampling, can lead to enhanced generalization and hence better reconstruction. Building on this insight, we propose two architecture-agnostic remedies: one to constrain the frequency range of the white-noise input and the other to penalize the Lipschitz constants of the network. We demonstrate that even with just one extra line of code on the input, the performance gap between the ill-designed models and the high-performing ones can be closed. These results signify that for the first time, architectural biases on untrained MRI reconstruction can be mitigated without architectural modifications.

翻译：以深度图像先验（Deep Image Prior，DIP）为代表的非训练神经网络，近期已能在无需全采样测量数据训练的条件下实现MRI重建。其成功被广泛归因于由合适网络架构所引发的隐式正则化。然而，对这种架构先验的理解不足导致了冗余的设计选择与次优结果。本研究旨在简化DIP-MRI的架构设计决策，以促进其实践部署。我们观察到，无论参数数量多少，某些架构组件更容易导致过拟合，并通过阻碍对未采集测量值的准确外推而产生严重的重建伪影。我们从频率角度解释这一现象，发现偏好低频的架构特征（即具有无学习上采样的深窄结构）能够提升泛化能力，从而获得更优的重建效果。基于这一见解，我们提出了两种与架构无关的补救措施：一是约束白噪声输入的频率范围，二是惩罚网络的Lipschitz常数。我们证明，即使仅在输入上添加一行额外代码，劣质模型与高性能模型之间的性能差距也能被消除。这些结果表明，首次实现了在不修改架构的情况下缓解非训练MRI重建中架构偏差的影响。