Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP), naturally fill this gap, but bring a host of new issues: the susceptibility to overfitting due to a lack of robust early stopping strategies and unstable convergence. We present a novel approach to tackle these issues by restricting DIP optimisation to a sparse linear subspace of its parameters, employing a synergy of dimensionality reduction techniques and second order optimisation methods. The low-dimensionality of the subspace reduces DIP's tendency to fit noise and allows the use of stable second order optimisation methods, e.g., natural gradient descent or L-BFGS. Experiments across both image restoration and tomographic tasks of different geometry and ill-posedness show that second order optimisation within a low-dimensional subspace is favourable in terms of optimisation stability to reconstruction fidelity trade-off.

翻译：深度学习已广泛用于解决图像重建任务，但由于高质量训练数据的短缺，其部署应用受到制约。无监督学习方法（如深度图像先验）自然填补了这一空白，但却带来一系列新问题：因缺乏稳健的早停策略而易陷入过拟合，以及收敛不稳定。我们提出一种新颖方法来解决这些问题，该方法将深度图像先验优化限制在其参数的稀疏线性子空间内，协同运用降维技术与二阶优化方法。子空间的低维特性降低了深度图像先验对噪声的拟合倾向，并允许使用稳定的二阶优化方法（如自然梯度下降或L-BFGS）。在具有不同几何构型和病态程度的图像恢复及层析成像任务上的实验表明：在低维子空间内进行二阶优化，有利于在优化稳定性与重建保真度之间取得更优权衡。