The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging including magnetic resonance imaging (MRI). However, conventional DIP suffers from severe overfitting and spectral bias effects. In this work, we first provide an analysis of how DIP recovers information from undersampled imaging measurements by analyzing the training dynamics of the underlying networks in the kernel regime for different architectures. This study sheds light on important underlying properties for DIP-based recovery. Current research suggests that incorporating a reference image as network input can enhance DIP's performance in image reconstruction compared to using random inputs. However, obtaining suitable reference images requires supervision, and raises practical difficulties. In an attempt to overcome this obstacle, we further introduce a self-driven reconstruction process that concurrently optimizes both the network weights and the input while eliminating the need for training data. Our method incorporates a novel denoiser regularization term which enables robust and stable joint estimation of both the network input and reconstructed image. We demonstrate that our self-guided method surpasses both the original DIP and modern supervised methods in terms of MR image reconstruction performance and outperforms previous DIP-based schemes for image inpainting.

翻译：深度图像先验（Deep Image Prior, DIP）能从残缺或失真测量值中重建高质量图像，使其在图像复原及包括磁共振成像（MRI）在内的医学成像逆问题中广受欢迎。然而，传统DIP存在严重的过拟合和频谱偏差效应。本文首先通过分析不同架构下底层网络在核机制中的训练动态，揭示了DIP如何从不充分采样的成像测量值中恢复信息。该研究为基于DIP的重建提供了重要的底层性质见解。目前研究表明，相较于使用随机输入，将参考图像作为网络输入可提升DIP在图像重建中的性能。然而，获取合适的参考图像需要监督信息，并在实际应用中带来困难。为克服此障碍，我们进一步提出一种自驱动重建过程，该过程在无需训练数据的情况下同步优化网络权重与输入。该方法引入新颖的去噪正则化项，实现了网络输入与重建图像的鲁棒联合估计。实验证明，我们的自引导方法在磁共振图像重建性能上超越了原始DIP和现代监督方法，并在图像修复任务中优于以往基于DIP的方案。