Plug-and-play algorithms constitute a popular framework for solving inverse imaging problems that rely on the implicit definition of an image prior via a denoiser. These algorithms can leverage powerful pre-trained denoisers to solve a wide range of imaging tasks, circumventing the necessity to train models on a per-task basis. Unfortunately, plug-and-play methods often show unstable behaviors, hampering their promise of versatility and leading to suboptimal quality of reconstructed images. In this work, we show that enforcing equivariance to certain groups of transformations (rotations, reflections, and/or translations) on the denoiser strongly improves the stability of the algorithm as well as its reconstruction quality. We provide a theoretical analysis that illustrates the role of equivariance on better performance and stability. We present a simple algorithm that enforces equivariance on any existing denoiser by simply applying a random transformation to the input of the denoiser and the inverse transformation to the output at each iteration of the algorithm. Experiments on multiple imaging modalities and denoising networks show that the equivariant plug-and-play algorithm improves both the reconstruction performance and the stability compared to their non-equivariant counterparts.

翻译：即插即用算法是解决逆成像问题的一种流行框架，其通过去噪器隐式定义图像先验。这类算法能够利用强大的预训练去噪器解决多种成像任务，避免了针对每个任务单独训练模型的必要性。然而，即插即用方法常表现出不稳定性，这限制了其通用性潜力并导致重建图像质量欠佳。本研究表明，强制去噪器对特定变换群（旋转、反射和/或平移）具有等变性，能显著提升算法的稳定性与重建质量。我们提供了理论分析，阐明等变性对提升性能与稳定性的作用。我们提出了一种简单算法，通过在每次迭代中对去噪器输入施加随机变换并对输出施加逆变换，即可使任意现有去噪器具备等变性。在多种成像模态与去噪网络上的实验表明，相较于非等变版本，等变即插即用算法在重建性能与稳定性方面均有提升。