Equivariant Imaging (EI) regularization has become the de-facto technique for unsupervised training of deep imaging networks, without any need of ground-truth data. Observing that the EI-based unsupervised training paradigm currently has significant computational redundancy leading to inefficiency in high-dimensional applications, we propose a sketched EI regularization which leverages the randomized sketching techniques for acceleration. We then extend our sketched EI regularization to develop an accelerated deep internal learning framework -- Sketched Equivariant Deep Image Prior (Sk.EI-DIP), which can be efficiently applied for single-image and task-adapted reconstruction. Our numerical study on X-ray CT image reconstruction tasks demonstrate that our approach can achieve order-of-magnitude computational acceleration over standard EI-based counterpart in single-input setting, and network adaptation at test time.

翻译：等变成像（EI）正则化已成为无需任何真实数据即可无监督训练深度成像网络的事实标准技术。观察到当前基于EI的无监督训练范式存在显著的计算冗余，导致高维应用中效率低下，我们提出了一种草图化EI正则化方法，该方法利用随机草图技术实现加速。随后，我们将草图化EI正则化扩展至加速深度内部学习框架——草图化等变深度图像先验（Sk.EI-DIP），该框架可高效应用于单图像及任务自适应重建。我们在X射线CT图像重建任务上的数值研究表明，在单输入设置及测试时网络自适应场景下，本方法相较于标准基于EI的对应方法可实现数量级计算加速。