Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results, these algorithms rely on a non-standard use of a denoiser on images that are less and less noisy along the iterations, which contrasts with recent algorithms based on Diffusion Models (DM), where the denoiser is applied only on re-noised images. We propose a new PnP framework, called Stochastic deNOising REgularization (SNORE), which applies the denoiser only on images with noise of the adequate level. It is based on an explicit stochastic regularization, which leads to a stochastic gradient descent algorithm to solve ill-posed inverse problems. A convergence analysis of this algorithm and its annealing extension is provided. Experimentally, we prove that SNORE is competitive with respect to state-of-the-art methods on deblurring and inpainting tasks, both quantitatively and qualitatively.

翻译：即插即用（PnP）算法是一类通过结合物理模型与深度神经网络进行正则化的迭代算法，用于解决图像逆问题。尽管这些算法能产生令人印象深刻的图像恢复结果，但它们依赖于一种非标准的去噪器应用方式——在迭代过程中对噪声逐渐减小的图像进行去噪，这与近期基于扩散模型（DM）的算法形成鲜明对比，后者仅对重新加噪的图像应用去噪器。我们提出了一种新的PnP框架，称为随机去噪正则化（SNORE），该框架仅在噪声水平适当的图像上应用去噪器。该方法基于显式随机正则化，进而导出用于求解病态逆问题的随机梯度下降算法。我们分析了该算法及其退火扩展的收敛性。实验表明，无论是在定量指标还是定性效果上，SNORE在去模糊和图像修复任务中均能与当前最先进方法相媲美。