DeepSN-Net: Deep Semi-smooth Newton Driven Network for Blind Image Restoration

The deep unfolding network represents a promising research avenue in image restoration. However, most current deep unfolding methodologies are anchored in first-order optimization algorithms, which suffer from sluggish convergence speed and unsatisfactory learning efficiency. In this paper, to address this issue, we first formulate an improved second-order semi-smooth Newton (ISN) algorithm, transforming the original nonlinear equations into an optimization problem amenable to network implementation. After that, we propose an innovative network architecture based on the ISN algorithm for blind image restoration, namely DeepSN-Net. To the best of our knowledge, DeepSN-Net is the first successful endeavor to design a second-order deep unfolding network for image restoration, which fills the blank of this area. Furthermore, it offers several distinct advantages: 1) DeepSN-Net provides a unified framework to a variety of image restoration tasks in both synthetic and real-world contexts, without imposing constraints on the degradation conditions. 2) The network architecture is meticulously aligned with the ISN algorithm, ensuring that each module possesses robust physical interpretability. 3) The network exhibits high learning efficiency, superior restoration accuracy and good generalization ability across 11 datasets on three typical restoration tasks. The success of DeepSN-Net on image restoration may ignite many subsequent works centered around the second-order optimization algorithms, which is good for the community.