# VSpSR: Explorable Super-Resolution via Variational Sparse Representation

arXiv: https://arxiv.org/abs/2104.08575 · HTML: https://mlsanity.com/paper/2104.08575/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 17 Apr 2021.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Real-Time Video Super-Resolution with Spatio-Temporal Networks and Motion Compensation](https://mlsanity.com/paper/1611.05250/) (2016)
- [Wide Activation for Efficient and Accurate Image Super-Resolution](https://mlsanity.com/paper/1808.08718/) (2018)
- [Explorable Super Resolution](https://mlsanity.com/paper/1912.01839/) (2019)
- [DeepSEE: Deep Disentangled Semantic Explorative Extreme Super-Resolution](https://mlsanity.com/paper/2004.04433/) (2020)
- [Understanding Deep Architectures using a Recursive Convolutional Network](https://mlsanity.com/paper/1312.1847/) (2013)

## Built on by (most cited first, 4 of 4)

- [Super-resolution Reconstruction of Single Image for Latent features](https://mlsanity.com/paper/2211.12845/) (2022)
- [Trustworthy SR: Resolving Ambiguity in Image Super-resolution via Diffusion Models and Human Feedback](https://mlsanity.com/paper/2402.07597/) (2024)
- [Diverse super-resolution with pretrained deep hiererarchical VAEs](https://mlsanity.com/paper/2205.10347/) (2022)
- [Enhancing Blind Face Restoration through Online Reinforcement Learning](https://mlsanity.com/paper/2509.23339/) (2025)

## Abstract (arXiv)

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