Training deep neural networks has become a common approach for addressing
image restoration problems. An alternative for training a "task-specific"
network for each observation model is to use pretrained deep denoisers for
imposing only the signal's prior within iterative algorithms, without
additional training. Recently, a sampling-based variant of this approach has
become popular with the rise of diffusion/score-based generative models. Using
denoisers for general purpose restoration requires guiding the iterations to
ensure agreement of the signal with the observations. In low-noise settings,
guidance that is based on back-projection (BP) has been shown to be a promising
strategy (used recently also under the names "pseudoinverse" or
"range/null-space" guidance). However, the presence of noise in the
observations hinders the gains from this approach. In this paper, we propose a
novel guidance technique, based on preconditioning that allows traversing from
BP-based guidance to least squares based guidance along the restoration scheme.
The proposed approach is robust to noise while still having much simpler
implementation than alternative methods (e.g., it does not require SVD or a
large number of iterations). We use it within both an optimization scheme and a
sampling-based scheme, and demonstrate its advantages over existing methods for
image deblurring and super-resolution.

训练深度神经网络已成为解决图像恢复问题的常用方法，本文提出了一种基于预条件的新型引导技术，它在恢复方案中的实现要比现有方法简单，同时对噪声具有抗干扰性，适用于图像去模糊和超分辨率的任务。