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（DIP）能从不完全或受损测量值中恢复高质量图像的能力，使其在图像修复和医学成像（包括磁共振成像（MRI））等逆问题中广受欢迎。然而，传统DIP存在严重的过拟合和频谱偏差效应。在本工作中，我们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的恢复方法的重要潜在特性提供了启示。当前研究表明，与使用随机输入相比，将参考图像作为网络输入可提升DIP在图像重建中的性能。但获取合适的参考图像需要监督信息，并带来实际困难。为克服这一障碍，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时优化网络权重和输入。我们的方法引入了一种新颖的去噪正则化项，能够稳健且稳定地联合估计网络输入和重建图像。实验表明，我们的自引导方法在MR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先前的DIP方案。