Untrained networks inspired by deep image prior have shown promising capabilities in recovering a high-quality image from noisy or partial measurements, without requiring training data. Their success has been widely attributed to the spectral bias acting as an implicit regularization induced by suitable network architectures. However, applications of such network-based priors often entail superfluous architectural decisions, overfitting risks, and slow optimization, all of which hinder their practicality. In this work, we propose efficient, architecture-agnostic methods for a more direct frequency control over the network priors: 1) constraining the bandwidth of the white-noise input, 2) controlling the bandwidth of the interpolation-based upsamplers, and 3) regularizing the Lipschitz constants of the layers. We show that even with just one extra line of code, the overfitting issues in underperforming architectures can be alleviated such that their performance gaps with the high-performing counterparts can be largely closed despite their distinct configurations, mitigating the need for architecture tuning. This then makes it possible to employ a more compact model to achieve similar or superior performance to larger models with greater efficiency. Our regularized network priors compare favorably with current supervised and self-supervised methods on MRI reconstruction and image inpainting tasks, serving as a stronger zero-shot baseline reconstructor. Our code will be made publicly available.

翻译：受深度图像先验启发的未训练网络在无需训练数据的情况下，从噪声或不完整测量中恢复高质量图像方面展现出显著能力。其成功被广泛归因于由合适网络架构诱导的频谱偏差作为隐式正则化机制。然而，此类基于网络先验的应用往往涉及冗余的架构选择、过拟合风险以及优化缓慢等问题，这些均阻碍了其实用性。在本工作中，我们提出了高效且架构无关的方法，以实现对网络先验更直接的频率控制：1）约束白噪声输入的带宽，2）控制基于插值的上采样器带宽，3）对各层的Lipschitz常数进行正则化。我们证明，即使仅增加一行额外代码，即可缓解表现不佳架构中的过拟合问题，使得尽管不同架构配置差异显著，其与高性能架构之间的性能差距得以大幅缩小，从而降低对架构调优的需求。这使得采用更紧凑的模型成为可能，以更高效率实现与大型模型相似甚至更优的性能。我们的正则化网络先验在MRI重建和图像修复任务中与当前监督及自监督方法相比表现优异，作为更强的零样本基线重建器。我们的代码将公开发布。