Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance
This addresses image restoration for applications like photography and medical imaging, offering a more robust and simpler alternative to existing guidance methods, though it appears incremental in advancing denoising diffusion models.
The paper tackles image restoration problems by proposing a novel guidance technique based on preconditioning that transitions between back-projection and least squares guidance, making it robust to noise while maintaining simple implementation. The approach demonstrates advantages over existing methods for image deblurring and super-resolution, though specific numerical improvements are not detailed in the abstract.
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.