# Fast Single Image Super-Resolution

arXiv: https://arxiv.org/abs/1510.00143 · HTML: https://mlsanity.com/paper/1510.00143/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2015.

## Built on by (most cited first, 10 of 10)

- [Fast and High-Quality Blind Multi-Spectral Image Pansharpening](https://mlsanity.com/paper/2103.09943/) (2021)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Deep Model-Based Super-Resolution with Non-uniform Blur](https://mlsanity.com/paper/2204.10109/) (2022)
- [Towards Interpretable Video Super-Resolution via Alternating Optimization](https://mlsanity.com/paper/2207.10765/) (2022)
- [CurvPnP: Plug-and-play Blind Image Restoration with Deep Curvature Denoiser](https://mlsanity.com/paper/2211.07286/) (2022)
- [CD-GAN: a robust fusion-based generative adversarial network for unsupervised remote sensing change detection with heterogeneous sensors](https://mlsanity.com/paper/2203.00948/) (2022)
- [Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels](https://mlsanity.com/paper/2210.10605/) (2022)
- [Identity-Preserving Pose-Robust Face Hallucination Through Face Subspace Prior](https://mlsanity.com/paper/2111.10634/) (2021)
- [Subspace-Based Feature Fusion From Hyperspectral And Multispectral Image For Land Cover Classification](https://mlsanity.com/paper/2102.11228/) (2021)
- [Analysis Plug-and-Play Methods for Imaging Inverse Problems](https://mlsanity.com/paper/2509.15422/) (2025)

## Abstract (arXiv)

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high resolution image from its blurred, decimated and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution can be obtained and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an ℓ2-regularized quadratic model, i.e., an ℓ2-ℓ2 optimization problem. Furthermore, the flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded intotraditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with the existing techniques.