The use of the convolutional neural network based prior in imaging inverse problems has become increasingly popular. Current state-of-the-art methods, however, can easily result in severe overfitting, which makes a number of early stopping techniques necessary to eliminate the overfitting problem. To motivate our work, we review some existing approaches to image priors. We find that the deep image prior in combined with the handcrafted prior has an outstanding performance in terms of interpretability and representability. We propose a multi-code deep image prior, a multiple latent codes variant of the deep image prior, which can be utilized to eliminate overfitting and is also robust to the different numbers of the latent codes. Due to the non-differentiability of the handcrafted prior, we use the alternative direction method of multipliers (ADMM) algorithm. We compare the performance of the proposed method on an image denoising problem and a highly ill-posed CT reconstruction problem against the existing state-of-the-art methods, including PnP-DIP, DIP-VBTV and ADMM DIP-WTV methods. For the CelebA dataset denoising, we obtain 1.46 dB peak signal to noise ratio improvement against all compared methods. For the CT reconstruction, the corresponding average improvement of three test images is 4.3 dB over DIP, and 1.7 dB over ADMM DIP-WTV, and 1.2 dB over PnP-DIP along with a significant improvement in the structural similarity index.

翻译：在成像逆问题中，基于卷积神经网络的先验知识应用日益普及。然而，当前最先进方法易导致严重过拟合，需采用多种早停技术来消除该问题。为启发本研究，我们回顾了现有图像先验方法，发现结合手工设计先验的深度图像先验在可解释性与表示能力方面表现优异。为此，我们提出多编码深度图像先验——深度图像先验的多潜在编码变体——该方案可消除过拟合现象，并对潜在编码数量差异具有鲁棒性。针对手工设计先验不可微的问题，采用交替方向乘子法（ADMM）算法。在图像去噪与高度病态CT重建问题上，我们将所提方法性能与现有最优方法（包括PnP-DIP、DIP-VBTV及ADMM DIP-WTV方法）进行对比。在CelebA数据集去噪任务中，峰值信噪比较所有对比方法提升1.46 dB；在CT重建任务中，三个测试图像的平均改善幅度分别为：较DIP提升4.3 dB，较ADMM DIP-WTV提升1.7 dB，较PnP-DIP提升1.2 dB，且结构相似性指标显著改善。