Convolutional Sparse Coding (CSC) has been attracting more and more attention in recent years, for making full use of image global correlation to improve performance on various computer vision applications. However, very few studies focus on solving CSC based image Super-Resolution (SR) problem. As a consequence, there is no significant progress in this area over a period of time. In this paper, we exploit the natural connection between CSC and Convolutional Neural Networks (CNN) to address CSC based image SR. Specifically, Convolutional Iterative Soft Thresholding Algorithm (CISTA) is introduced to solve CSC problem and it can be implemented using CNN architectures. Then we develop a novel CSC based SR framework analogy to the traditional SC based SR methods. Two models inspired by this framework are proposed for pre-/post-upsampling SR, respectively. Compared with recent state-of-the-art SR methods, both of our proposed models show superior performance in terms of both quantitative and qualitative measurements.
This work exploits the natural connection between CSC and Convolutional Neural Networks (CNN) to address CSC based image SR. Specifically, Convolutional Iterative Soft Thresholding Algorithm (CISTA) is introduced to solve CSC problem and state-of-the-art performance is achieved on popular benchmarks.
[Strengths]
- This paper is well-written and easy to follow.
[Weaknesses]
- My main concern on this work is its novelty seems to be limited. In Introduction, the authors raised 4 kinds of issues, including framework/optimization/memory/multi-scale. However, optimization and memory issues are mitigated by the CNN architectures; multi-scale issue is addressed with the help of work from Kim et al.. It seems the proposed questions are mostly addressed by the previous methods.
- It seems CISTA may be the main novelty of this work. However, no comparasions with previous ISTA methods (e.g., [R1-3]) are conducted and discussed. 
- From Tabs. 2&3, the improvement is very limited. Besides, time complexity needs to be compared with the competitors, including flops or inference times.
[R1] A Fast Proximal Method for Convolutional Sparse Coding, IJCNN 2013.
[R2] Convolutional Neural Networks Analyzed via Convolutional Sparse Coding, JMLR 2017.
[R3] On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks, TPAMI 2018.