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Super-resolution (SR) is an ill-posed problem, which means that infinitelymany high-resolution (HR) images can be degraded to the same low-resolution(LR) image. To study the one-to-many stochastic SR mapping, we implicitlyrepresent the non-local self-similarity of natural images and develop aVariational Sparse framework for Super-Resolution (VSpSR) via neural networks.Since every small patch of a HR image can be well approximated by the sparserepresentation of atoms in an over-complete dictionary, we design a two-branchmodule, i.e., VSpM, to explore the SR space. Concretely, one branch of VSpMextracts patch-level basis from the LR input, and the other branch inferspixel-wise variational distributions with respect to the sparse coefficients.By repeatedly sampling coefficients, we could obtain infinite sparserepresentations, and thus generate diverse HR images. According to thepreliminary results of NTIRE 2021 challenge on learning SR space, our team(FudanZmic21) ranks 7-th in terms of released scores. The implementation ofVSpSR is released at https://zmiclab.github.io/.

VSpSR: Explorable Super-Resolution via Variational Sparse Representation