Deep Non-Blind Deconvolution via Generalized Low-Rank Approximation
In this paper, we present a deep convolutional neural network to capture the inherent properties of image degradation, which can handle different kernels and saturated pixels in a unified framework. The proposed neural network is motivated by the low-rank property of pseudo-inverse kernels. Specifically, we first compute a generalized low-rank approximation to a large number of blur kernels, and then use separable filters to initialize the convolutional parameters in the network. Our analysis shows that the estimated decomposed matrices contain the most essential information of an input kernel, which ensures the proposed network to handle various blurs in a unified framework and generate high-quality deblurring results. Experimental results on benchmark datasets with noisy and saturated pixels demonstrate that the proposed deconvolution approach relying on generalized low-rank approximation performs favorably against the state-of-the-arts.
This paper extends the non-blind deconvolution in [1]. The author proposes to use a generalized low-rank approximation method to model a wide range of blur kernels and train the non-blind deconvolution network with the low-rank representation.  Strength: - Unlike the model in [1] that requires a specific training (or fine tuning) for each kernel, the proposed model can handle different blur kernels. - The model can use the low-rank representation results to initialize the model parameters. - Experiments show that the model can achieve good performances on different images and performs better than the compared methods, such as [1].  Weakness: - The most important motivation of this paper is to make the learning-based CNN model being able to handle different kernels. I did not find the reason for using the low-rank approximation-based method. Regarding the extension of the model in [1], I agree the low-rank representation idea is straightforward and clever, but, generally, I am wondering whether building a pre-defined and restricted representation for kernels is necessary. In many optimization-based neural network design, the blur kernels can be directly fed into a learnable neural network. Please check [2,3]. They both can work as a flexible model for different kernels and perform very well for different images. I want to see the discussions and comparisons (if possible) with these neural networks motivated by the conventional optimizer.   - The author may experiment to study the sensitivity of the proposed model to the noise. - More experiments on the standard non-blind deconvolution benchmark datasets are necessary to validate the proposed method.   [1] L. Xu, J. S. Ren, C. Liu, and J. Jia. Deep convolutional neural network for image deconvolution. In NIPS, 2014.  [2] Kruse, Jakob, Carsten Rother, and Uwe Schmidt. "Learning to push the limits of efficient fft-based image deconvolution." IEEE International Conference on Computer Vision (ICCV). 2017. [3] Gong, D., Zhang, Z., Shi, Q., Hengel, A. V. D., Shen, C., & Zhang, Y. (2018). Learning an Optimizer for Image Deconvolution. arXiv preprint arXiv:1804.03368. [4] Zhang, K., Zuo, W., Gu, S., & Zhang, L. (2017, July). Learning deep CNN denoiser prior for image restoration. In IEEE Conference on Computer Vision and Pattern Recognition (Vol. 2).  The authors address my major concerns. I tend to vote for acceptance.