Towards Architecture-Insensitive Untrained Network Priors for Accelerated MRI Reconstruction

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.