One key ingredient of image restoration is to define a realistic prior on clean images to complete the missing information in the observation. State-of-the-art restoration methods rely on a neural network to encode this prior. Moreover, typical image distributions are invariant to some set of transformations, such as rotations or flips. However, most deep architectures are not designed to represent an invariant image distribution. Recent works have proposed to overcome this difficulty by including equivariance properties within a Plug-and-Play paradigm. In this work, we propose a unified framework named Equivariant Regularization by Denoising (ERED) based on equivariant denoisers and stochastic optimization. We analyze the convergence of this algorithm and discuss its practical benefit.

翻译：图像复原的一个关键要素是定义干净图像的真实先验，以补全观测中缺失的信息。最先进的复原方法依赖神经网络来编码这种先验。此外，典型的图像分布对某些变换集合（如旋转或翻转）具有不变性。然而，大多数深度架构并非为表示不变图像分布而设计。近期研究提出通过将等变特性纳入即插即用范式来克服这一困难。本工作提出一个名为"等变去噪正则化"的统一框架，该框架基于等变去噪器与随机优化方法。我们分析了该算法的收敛性并讨论了其实际优势。