mlsanityData to 7 Oct 2026

Super-Resolution Neural Operator

arXiv 2303.02584 ↗First posted 5 Mar 2023cs.CVcited by 48

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Abstract (arXiv)

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous functions approximated with different grid sizes, SRNO learns the mapping between the corresponding function spaces. From the perspective of approximation theory, SRNO first embeds the LR input into a higher-dimensional latent representation space, trying to capture sufficient basis functions, and then iteratively approximates the implicit image function with a kernel integral mechanism, followed by a final dimensionality reduction step to generate the RGB representation at the target coordinates. The key characteristics distinguishing SRNO from prior continuous SR works are: 1) the kernel integral in each layer is efficiently implemented via the Galerkin-type attention, which possesses non-local properties in the spatial domain and therefore benefits the grid-free continuum; and 2) the multilayer attention architecture allows for the dynamic latent basis update, which is crucial for SR problems to "hallucinate" high-frequency information from the LR image. Experiments show that SRNO outperforms existing continuous SR methods in terms of both accuracy and running time. Our code is at https://github.com/2y7c3/Super-Resolution-Neural-Operator

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 30 of its 43 references that are in the map. First posted on arXiv 5 Mar 2023.

Builds on

30 of 43 references.

References · 30

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  4. 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
  5. 2020Training data-efficient image transformers & distillation through attentioncited by 4,560
  6. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  7. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  8. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  9. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  10. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  11. 2021SwinIR: Image Restoration Using Swin Transformercited by 1,869
  12. 2017Enhanced Deep Residual Networks for Single Image Super-Resolutioncited by 1,543
18 more
  1. 2018Image Super-Resolution Using Very Deep Residual Channel Attention Networkscited by 1,256
  2. 2016Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Networkcited by 1,199
  3. 2020Pre-Trained Image Processing Transformercited by 891
  4. 2018Residual Dense Network for Image Super-Resolutioncited by 796
  5. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  6. 2020Learning Continuous Image Representation with Local Implicit Image Functioncited by 550
  7. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  8. 2021Choose a Transformer: Fourier or Galerkincited by 333
  9. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
  10. 2019Meta-SR: A Magnification-Arbitrary Network for Super-Resolutioncited by 180
  11. 2020How Much Position Information Do Convolutional Neural Networks Encode?cited by 171
  12. 2020Interpreting Super-Resolution Networks with Local Attribution Mapscited by 136
  13. 2021Local Texture Estimator for Implicit Representation Functioncited by 126
  14. 2020MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Frameworkcited by 78
  15. 2020Learning A Single Network for Scale-Arbitrary Super-Resolutioncited by 65
  16. 2021Implicit Transformer Network for Screen Content Image Continuous Super-Resolutioncited by 46
  17. 2021Solving PDE-constrained Control Problems Using Operator Learningcited by 41
  18. 2021SRWarp: Generalized Image Super-Resolution under Arbitrary Transformationcited by 26

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 15; 2025: 16; 2026: 14.

48 papers.

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  1. 2025Pixel to Gaussian: Ultra-Fast Continuous Super-Resolution with 2D Gaussian Modelingcited by 47
  2. 2025Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systemscited by 29
  3. 2025Generalized and Efficient 2D Gaussian Splatting for Arbitrary-scale Super-Resolutioncited by 21
  4. 2024Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discoverycited by 18
  5. 2024Basis-to-Basis Operator Learning Using Function Encoderscited by 17
  6. 2024HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolutioncited by 17
  7. 2024DiffFNO: Diffusion Fourier Neural Operatorcited by 13
  8. 2023TULIP: Transformer for Upsampling of LiDAR Point Cloudscited by 12
  9. 2024S3Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Modelcited by 12
  10. 2024Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolutioncited by 11
  11. 2024Exploring the Low-Pass Filtering Behavior in Image Super-Resolutioncited by 7
  12. 2023Thera: Aliasing-Free Arbitrary-Scale Super-Resolution with Neural Heat Fieldscited by 5
36 more
  1. 2025VQualA 2025 Challenge on Image Super-Resolution Generated Content Quality Assessment: Methods and Resultscited by 5
  2. 2024Learning Dual-Level Deformable Implicit Representation for Real-World Scale Arbitrary Super-Resolutioncited by 3
  3. 2024Space-Time Video Super-resolution with Neural Operatorcited by 3
  4. 2024AnySR: Realizing Image Super-Resolution as Any-Scale, Any-Resourcecited by 3
  5. 2024Solving Differential Equations with Constrained Learningcited by 3
  6. 2025NeurOp-Diff:Continuous Remote Sensing Image Super-Resolution via Neural Operator Diffusioncited by 3
  7. 2024MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolutioncited by 2
  8. 2025Localized FNO for Spatiotemporal Hemodynamic Upsampling in Aneurysm MRIcited by 2
  9. 2025Locally Adaptive Conformal Inference for Operator Modelscited by 2
  10. 2024Adaptive Multi-modal Fusion of Spatially Variant Kernel Refinement with Diffusion Model for Blind Image Super-Resolutioncited by 1
  11. 2024LeRF: Learning Resampling Function for Adaptive and Efficient Image Interpolationcited by 1
  12. 2025Reconstruct Anything Model: a lightweight general model for computational imagingcited by 1
  13. 2025AnyTSR: Any-Scale Thermal Super-Resolution for UAVcited by 1
  14. 2025SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Samplingcited by 1
  15. 2025Radiative-Structured Neural Operator for Continuous Spectral Super-Resolutioncited by 1
  16. 2026Beyond Visual Fidelity: Benchmarking Super-Resolution Models for Large-Scale Remote Sensing Imagery via Downstream Task Integrationcited by 1
  17. 2023A Unified Framework to Super-Resolve Face Images of Varied Low Resolutionscited by 0
  18. 2024Multi-modal Representation Learning for Cross-modal Prediction of Continuous Weather Patterns from Discrete Low-Dimensional Datacited by 0
  19. 2025Frequency-Integrated Transformer for Arbitrary-Scale Super-Resolutioncited by 0
  20. 2025Stroke-based Cyclic Amplifier: Image Super-Resolution at Arbitrary Ultra-Large Scalescited by 0
  21. 2025A Neural Operator based on Dynamic Mode Decompositioncited by 0
  22. 2025JPEG Processing Neural Operator for Backward-Compatible Codingcited by 0
  23. 2025History-Augmented Contrastive Learning With Soft Mixture of Experts for Blind Super-Resolution of Planetary Remote Sensing Imagescited by 0
  24. 2026Implicit Neural Representation-Based Continuous Single Image Super-Resolution: An Empirical Benchmarkcited by 0
  25. 2026Neuro-Symbolic Multitasking: A Unified Framework for Discovering Generalizable Solutions to PDE Familiescited by 0
  26. 2026High-Resolution Climate Projections Using Diffusion-Based Downscaling of a Lightweight Climate Emulatorcited by 0
  27. 2026UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learningcited by 0
  28. 2026Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurringcited by 0
  29. 2026GB-LSR: Local Spectral Decoding with a Learned Global Bandwidth for Arbitrary-Scale Super-Resolutioncited by 0
  30. 2026Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolutioncited by 0
  31. 2026Adaptive Densification for High-Fidelity and Efficient Sparse Gaussian Splatting in Arbitrary-Scale Super-Resolutioncited by 0
  32. 2026Resonant Brane Splatting for Arbitrary-Scale Super-Resolutioncited by 0
  33. 2026A neural operator view on U-Nets for inverse imaging problemscited by 0
  34. 2026RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solverscited by 0
  35. 2026Spectral Super-Resolution using Spatial-Spectral Residual Operator Networkscited by 0
  36. 2026Super-Resolving Unseen Hyperspectral Sensors at Any Scale via Spatial Operatorscited by 0