mlsanityData to 14 Oct 2026

Revisiting L1 Loss in Super-Resolution: A Probabilistic View and Beyond

arXiv 2201.10084 ↗First posted 25 Jan 2022cs.CVcited by 5

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Abstract (arXiv)

Super-resolution as an ill-posed problem has many high-resolution candidates for a low-resolution input. However, the popular ℓ1 loss used to best fit the given HR image fails to consider this fundamental property of non-uniqueness in image restoration. In this work, we fix the missing piece in ℓ1 loss by formulating super-resolution with neural networks as a probabilistic model. It shows that ℓ1 loss is equivalent to a degraded likelihood function that removes the randomness from the learning process. By introducing a data-adaptive random variable, we present a new objective function that aims at minimizing the expectation of the reconstruction error over all plausible solutions. The experimental results show consistent improvements on mainstream architectures, with no extra parameter or computing cost at inference time.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 48 of its 102 references that are in the map. First posted on arXiv 25 Jan 2022.

Builds on

48 of 102 references.

References · 48

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  4. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  5. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,694
  6. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,908
  7. 2021SwinIR: Image Restoration Using Swin Transformercited by 1,887
  8. 2017Enhanced Deep Residual Networks for Single Image Super-Resolutioncited by 1,552
  9. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
  10. 2018Image Super-Resolution Using Very Deep Residual Channel Attention Networkscited by 1,264
  11. 2017Deep Image Priorcited by 1,098
  12. 2015Accurate Image Super-Resolution Using Very Deep Convolutional Networkscited by 903
36 more
  1. 2020Pre-Trained Image Processing Transformercited by 893
  2. 2018Residual Dense Network for Image Super-Resolutioncited by 799
  3. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 533
  4. 2017FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoisingcited by 510
  5. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  6. 2016Tutorial on Variational Autoencoderscited by 409
  7. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 408
  8. 2019Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Modelcited by 403
  9. 2016Accelerating the Super-Resolution Convolutional Neural Networkcited by 394
  10. 2020Learning Texture Transformer Network for Image Super-Resolutioncited by 347
  11. 2015Sketch-based Manga Retrieval using Manga109 Datasetcited by 329
  12. 2015Deeply-Recursive Convolutional Network for Image Super-Resolutioncited by 317
  13. 2015Deep multi-scale video prediction beyond mean square errorcited by 300
  14. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
  15. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 276
  16. 2020Single Image Super-Resolution via a Holistic Attention Networkcited by 265
  17. 2018Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Networkcited by 264
  18. 2019Residual Non-local Attention Networks for Image Restorationcited by 236
  19. 2019Lightweight Image Super-Resolution with Information Multi-distillation Networkcited by 227
  20. 2016Generating Images with Perceptual Similarity Metrics based on Deep Networkscited by 222
  21. 2015Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networkscited by 214
  22. 2018Multi-level Wavelet-CNN for Image Restorationcited by 184
  23. 2019Real Image Denoising with Feature Attentioncited by 176
  24. 2018Non-Local Recurrent Network for Image Restorationcited by 160
  25. 2016Real-Time Video Super-Resolution with Spatio-Temporal Networks and Motion Compensationcited by 156
  26. 2018Fast and Accurate Single Image Super-Resolution via Information Distillation Networkcited by 121
  27. 2018Neural Nearest Neighbors Networkscited by 98
  28. 2020Cross-Scale Internal Graph Neural Network for Image Super-Resolutioncited by 94
  29. 2018Bayesian Uncertainty Estimation for Batch Normalized Deep Networkscited by 70
  30. 2018Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected Networkcited by 64
  31. 2020Learning with Privileged Information for Efficient Image Super-Resolutioncited by 53
  32. 2016Deep Gaussian Processes for Regression using Approximate Expectation Propagationcited by 39
  33. 2015Super-Resolution with Deep Convolutional Sufficient Statisticscited by 35
  34. 2019Deep Graph-Convolutional Image Denoisingcited by 32
  35. 2018Identifying Recurring Patterns with Deep Neural Networks for Natural Image Denoisingcited by 16
  36. 2015Learning Super-Resolution Jointly from External and Internal Examplescited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 1.

5 papers.

  1. 2024TSD-SR: One-Step Diffusion with Target Score Distillation for Real-World Image Super-Resolutioncited by 87
  2. 2023Noise-free Optimization in Early Training Steps for Image Super-Resolutioncited by 3
  3. 2025QUIET-SR: Quantum Image Enhancement Transformer for Single Image Super-Resolutioncited by 2
  4. 2025A Classification-Aware Super-Resolution Framework for Ship Targets in SAR Imagerycited by 1
  5. 2026Interest Entanglement: The Hidden Barrier to Blind Super-Resolution Optimizationcited by 0