mlsanityData to 7 Oct 2026

Solving Image PDEs with a Shallow Network

arXiv 2110.08327 ↗First posted 15 Oct 2021cs.CV cs.LG eess.IVcited by 1

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Abstract (arXiv)

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for solving PDEs tend to require very fine grid resolution for stability, and as a result have impractically high computational cost. This work applies BLADE (Best Linear Adaptive Enhancement), a shallow learnable filtering framework, to PDE solving, and shows that the resulting approach is efficient and accurate, operating more reliably at coarse grid resolutions than classical methods. As such, the model can be flexibly used for a wide variety of problems in imaging.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 32 references that are in the map. First posted on arXiv 15 Oct 2021.

Builds on

16 of 32 references.

References · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,678
  4. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
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  6. 2017PDE-Net: Learning PDEs from Datacited by 304
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  8. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  9. 2019Handheld Multi-Frame Super-Resolutioncited by 85
  10. 2017Multi-level Residual Networks from Dynamical Systems Viewcited by 59
  11. 2018DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecastcited by 28
  12. 2016RAISR: Rapid and Accurate Image Super Resolutioncited by 27
4 more
  1. 2017Learned Perceptual Image Enhancementcited by 18
  2. 2017BLADE: Filter Learning for General Purpose Computational Photographycited by 12
  3. 2018Approximating the solution to wave propagation using deep neural networkscited by 8
  4. 2018Fast, Trainable, Multiscale Denoisingcited by 2

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Cited by year

Citing papers per year: 2022: 1.

1 paper.

  1. 2022Unsupervised Learning of the Total Variation Flowcited by 3