# Deep Constrained Least Squares for Blind Image Super-Resolution

arXiv: https://arxiv.org/abs/2202.07508 · HTML: https://mlsanity.com/paper/2202.07508/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [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)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [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)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform](https://mlsanity.com/paper/1804.02815/) (2018)
- [Sketch-based Manga Retrieval using Manga109 Dataset](https://mlsanity.com/paper/1510.04389/) (2015)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Learning a Single Convolutional Super-Resolution Network for Multiple Degradations](https://mlsanity.com/paper/1712.06116/) (2017)
- [Deep Back-Projection Networks For Super-Resolution](https://mlsanity.com/paper/1803.02735/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Blind Super-Resolution With Iterative Kernel Correction](https://mlsanity.com/paper/1904.03377/) (2019)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Feedback Network for Image Super-Resolution](https://mlsanity.com/paper/1903.09814/) (2019)
- [Unfolding the Alternating Optimization for Blind Super Resolution](https://mlsanity.com/paper/2010.02631/) (2020)
- [Meta-Transfer Learning for Zero-Shot Super-Resolution](https://mlsanity.com/paper/2002.12213/) (2020)

## Built on by (most cited first, 30 of 47)

- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Models](https://mlsanity.com/paper/2304.08291/) (2023)
- [Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution](https://mlsanity.com/paper/2309.00287/) (2023)
- [BSRT: Improving Burst Super-Resolution with Swin Transformer and Flow-Guided Deformable Alignment](https://mlsanity.com/paper/2204.08332/) (2022)
- [Knowledge Distillation based Degradation Estimation for Blind Super-Resolution](https://mlsanity.com/paper/2211.16928/) (2022)
- [HST: Hierarchical Swin Transformer for Compressed Image Super-resolution](https://mlsanity.com/paper/2208.09885/) (2022)
- [DIPNet: Efficiency Distillation and Iterative Pruning for Image Super-Resolution](https://mlsanity.com/paper/2304.07018/) (2023)
- [Efficient Test-Time Adaptation for Super-Resolution with Second-Order Degradation and Reconstruction](https://mlsanity.com/paper/2310.19011/) (2023)
- [A Dynamic Kernel Prior Model for Unsupervised Blind Image Super-Resolution](https://mlsanity.com/paper/2404.15620/) (2024)
- [Degradation-Aware Self-Attention Based Transformer for Blind Image Super-Resolution](https://mlsanity.com/paper/2310.04180/) (2023)
- [Towards Lightweight Super-Resolution with Dual Regression Learning](https://mlsanity.com/paper/2207.07929/) (2022)
- [CFAT: Unleashing TriangularWindows for Image Super-resolution](https://mlsanity.com/paper/2403.16143/) (2024)
- [Joint Learning Content and Degradation Aware Feature for Blind Super-Resolution](https://mlsanity.com/paper/2208.13436/) (2022)
- [End-to-end Alternating Optimization for Real-World Blind Super Resolution](https://mlsanity.com/paper/2308.08816/) (2023)
- [CDFormer:When Degradation Prediction Embraces Diffusion Model for Blind Image Super-Resolution](https://mlsanity.com/paper/2405.07648/) (2024)
- [Better "CMOS" Produces Clearer Images: Learning Space-Variant Blur Estimation for Blind Image Super-Resolution](https://mlsanity.com/paper/2304.03542/) (2023)
- [Dual-Diffusion: Dual Conditional Denoising Diffusion Probabilistic Models for Blind Super-Resolution Reconstruction in RSIs](https://mlsanity.com/paper/2305.12170/) (2023)
- [VCISR: Blind Single Image Super-Resolution with Video Compression Synthetic Data](https://mlsanity.com/paper/2311.00996/) (2023)
- [Fast Nearest Convolution for Real-Time Efficient Image Super-Resolution](https://mlsanity.com/paper/2208.11609/) (2022)
- [Training-Free Model Ensemble for Single-Image Super-Resolution via Strong-Branch Compensation](https://mlsanity.com/paper/2604.11564/) (2026)
- [BlindDiff: Empowering Degradation Modelling in Diffusion Models for Blind Image Super-Resolution](https://mlsanity.com/paper/2403.10211/) (2024)
- [Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching](https://mlsanity.com/paper/2506.14605/) (2025)
- [Blind Video Super-Resolution based on Implicit Kernels](https://mlsanity.com/paper/2503.07856/) (2025)
- [Sliding Window Recurrent Network for Efficient Video Super-Resolution](https://mlsanity.com/paper/2208.11608/) (2022)
- [Equipping Diffusion Models with Differentiable Spatial Entropy for Low-Light Image Enhancement](https://mlsanity.com/paper/2404.09735/) (2024)
- [Efficient Image Super-Resolution via Symmetric Visual Attention Network](https://mlsanity.com/paper/2401.08913/) (2024)
- [Suppressing Uncertainties in Degradation Estimation for Blind Super-Resolution](https://mlsanity.com/paper/2406.16459/) (2024)
- [MF-LPR2: Multi-Frame License Plate Image Restoration and Recognition using Optical Flow](https://mlsanity.com/paper/2508.14797/) (2025)
- [EgoVSR: Towards High-Quality Egocentric Video Super-Resolution](https://mlsanity.com/paper/2305.14708/) (2023)
- [SAM-IQA: Can Segment Anything Boost Image Quality Assessment?](https://mlsanity.com/paper/2307.04455/) (2023)

## Abstract (arXiv)

In this paper, we tackle the problem of blind image super-resolution(SR) with a reformulated degradation model and two novel modules. Following the common practices of blind SR, our method proposes to improve both the kernel estimation as well as the kernel-based high-resolution image restoration. To be more specific, we first reformulate the degradation model such that the deblurring kernel estimation can be transferred into the low-resolution space. On top of this, we introduce a dynamic deep linear filter module. Instead of learning a fixed kernel for all images, it can adaptively generate deblurring kernel weights conditional on the input and yield a more robust kernel estimation. Subsequently, a deep constrained least square filtering module is applied to generate clean features based on the reformulation and estimated kernel. The deblurred feature and the low input image feature are then fed into a dual-path structured SR network and restore the final high-resolution result. To evaluate our method, we further conduct evaluations on several benchmarks, including Gaussian8 and DIV2KRK. Our experiments demonstrate that the proposed method achieves better accuracy and visual improvements against state-of-the-art methods.