  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.
