Paper:
Non-Local Recurrent Network for Image Restoration
Many classic methods have shown non-local self-similarity in natural images to be an effective prior for image restoration. However, it remains unclear and challenging to make use of this intrinsic property via deep networks. In this paper, we propose a non-local recurrent network (NLRN) as the first attempt to incorporate non-local operations into a recurrent neural network (RNN) for image restoration. The main contributions of this work are: (1) Unlike existing methods that measure self-similarity in an isolated manner, the proposed non-local module can be flexibly integrated into existing deep networks for end-to-end training to capture deep feature correlation between each location and its neighborhood. (2) We fully employ the RNN structure for its parameter efficiency and allow deep feature correlation to be propagated along adjacent recurrent states. This new design boosts robustness against inaccurate correlation estimation due to severely degraded images. (3) We show that it is essential to maintain a confined neighborhood for computing deep feature correlation given degraded images. This is in contrast to existing practice [41] that deploys the whole image. Extensive experiments on both image denoising and super-resolution tasks are conducted. Thanks to the recurrent non-local operations and correlation propagation, the proposed NLRN achieves superior results to state-of-the-art methods with many fewer parameters. The code is available at https://github.com/Ding-Liu/NLRN.

Review:
This paper introduced a mathematical framework to describe nonlocal operations in image restoration, such as nonlocal means, low-rank models, etc. Then the authors use the framework as a module of an RNN and validated the network on a few datasets for image denoising and super-resolution. Overall, I see merits of this paper, while I have a few questions/concerns. (See below.)  Pros:  1) The proposed framework is a nice summary of exsiting nonlocal operations commonly used in image restoration.  2) The proposed deep model works epseically well on texture images, and has advantage over several exsiting models.   Cons:  1) It has already known to the literature that some nonlocal operations can be put in matrix/operator forms. The authors claims they were the first to propose such framework. However, I think they should address the relation and differences between their framework and existing ones, such as the ones listed below: -- Yin, Rujie, et al. "A tale of two bases: Local-nonlocal regularization on image patches with convolution framelets." SIAM Journal on Imaging Sciences 10.2 (2017): 711-750. -- Danielyan, Aram, Vladimir Katkovnik, and Karen Egiazarian. "BM3D frames and variational image deblurring." IEEE Transactions on Image Processing 21.4 (2012): 1715-1728.  2) The authors emphasized a multiple places as one of their contributions that local search regions for similarity should be used. This is one of the main differences between their model with [37]. However, such treatment is a common practice for nonlocal means. The other two differences from [37] seems minor. From the title of the paper, the non-localness is the main selling point of the paper, which has already appeared in [37].  3) In the mathematical framework, the use of correlation features is not included. However, it appears in RNN model. From Table 2, with or without correlation propergation does not seem to make much difference. Then why bother introducing the additional path of s_corr in the network? I might have misinterpreted the paper, but in any case, I think this should be further clarified.   4) How does the proposed network compare with some exsiting nonlocal+dl denoising models such as  Lefkimmiatis, Stamatios. "Non-local color image denoising with convolutional neural networks." In Proc. IEEE Int. Conf. Computer Vision and Pattern Recognition, pp. 3587-3596. 2017.