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：即插即用算法构成了一种解决逆成像问题的流行框架，该框架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广泛的成像任务，无需针对每个任务单独训练模型。然而，即插即用方法常表现出不稳定性，阻碍了其通用性前景并导致重建图像质量欠佳。本研究表明，在去噪器上强制执行对特定变换群（旋转、反射和/或平移）的等变性，可显著提升算法稳定性与重建质量。我们通过理论分析阐明了等变性对改善性能与稳定性的作用，并提出一种简单算法：只需在算法每次迭代时对去噪器输入施加随机变换，并对输出施加逆变换，即可赋予任何现有去噪器等变性。针对多种成像模态与去噪网络的实验表明，与非等变方法相比，等变即插即用算法在重建性能与稳定性方面均有提升。