Equivariant Denoisers for Plug and Play Image Restoration

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. 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 two unified frameworks named Equivariant Regularization by Denoising (ERED) and Equivariant Plug-and-Play (EPnP) based on equivariant denoisers and stochastic optimization. We analyze the convergence of the proposed algorithms and discuss their practical benefit.