The deep image prior (DIP) is a state-of-the-art unsupervised approach for solving linear inverse problems in imaging. We address two key issues that have held back practical deployment of the DIP: the long computing time needed to train a separate deep network per reconstruction, and the susceptibility to overfitting due to a lack of robust early stopping strategies in the unsupervised setting. To this end, we restrict DIP optimisation to a sparse linear subspace of the full parameter space. We construct the subspace from the principal eigenspace of a set of parameter vectors sampled at equally spaced intervals during DIP pre-training on synthetic task-agnostic data. The low-dimensionality of the resulting subspace reduces DIP's capacity to fit noise and allows the use of fast second order optimisation methods, e.g., natural gradient descent or L-BFGS. Experiments across tomographic tasks of different geometry, ill-posedness and stopping criteria consistently show that second order optimisation in a subspace is Pareto-optimal in terms of optimisation time to reconstruction fidelity trade-off.

翻译：深度图像先验（DIP）是一种用于解决图像线性逆问题的先进无监督方法。针对阻碍DIP实际部署的两个关键问题：每次重建需单独训练深度网络导致的计算时间过长，以及无监督场景下因缺乏稳健早期停止策略而易过拟合，我们提出将DIP优化限制在全参数空间的稀疏线性子空间中。该子空间通过预训练（基于合成任务无关数据）过程中以等间隔采样的参数向量集的生成特征空间构建。子空间的低维性降低了DIP拟合噪声的能力，并支持快速二阶优化方法（例如自然梯度下降或L-BFGS）。在不同几何形态、病态程度及停止准则的层析成像任务实验中，子空间内的二阶优化始终在优化时间与重建保真度的权衡中达到帕累托最优。