[Neurocomputing'25] SoFoNO : Arbitrary-Scale Image Super-Resolution via Sobolev Fourier Neural Operator

📝 Authors: Jong Kwon Oh^{a, 1}, Hwijae Son^{b, 1}, Hyung Ju Hwang^a, and Jihyong Oh^{c, *}

🎓 Institution:

• ^a Pohang University of Science and Technology (POSTECH)
• ^b Konkuk University
• ^c Chung-Ang University

🧾 Author Notes:

• ¹ These authors contributed equally (co-first authors).
• ^* Corresponding author

This repository contains the official implementation for SoFoNO introduced in the following paper:

Software Environment

This project was implemented and tested with the following software configuration:

• Python: 3.9
• PyTorch: 2.6.0
• Torchvision: 0.21.0
• CUDA: 12.4
• cuDNN: 9.1.0.70
• NumPy: 2.0.2
• SciPy: 1.13.1
• OpenCV: 4.11.0.86

Hardware

• GPU: Single NVIDIA A100 80GB

Download Dataset

To download and prepare the DIV2K dataset for training and validation, follow these steps:

1. Create a data directory and navigate into it:

   mkdir data
   cd data

2. Download the DIV2K train and validation datasets:

   wget http://data.vision.ee.ethz.ch/cvl/DIV2K/DIV2K_train_HR.zip
   wget http://data.vision.ee.ethz.ch/cvl/DIV2K/DIV2K_valid_HR.zip

3. Unzip the downloaded files:

   unzip DIV2K_train_HR.zip
   unzip DIV2K_valid_HR.zip
   

Train

python train.py --config configs/train_edsr-SoFoNO.yaml If you want to change SoFoNO's argument, please modify the yaml file.

model:
  name: sofono
  args:
    encoder_spec:
      name: edsr-baseline
      args:
        no_upsampling: true
    width: 256
    T : 3
    ranges : [-1, 1]
    local_branch : Conv
    init_s : 0.0

Test

Download a DIV2K pre-trained model.

Model	Download
SoFoNO	Google Drive

python test.py --config configs/test_SoFoNO.yaml --mcell True You should input the test data and model information into the yaml file.

test_dataset:
  dataset:
    name: image-folder
    args:
      root_path: ./data/DIV2K_valid_HR
  wrapper:
      name: sr-implicit-downsampled-fast
      args:
        scale_min: 4
        scale_max: 4
        ranges : [-1, 1]
  batch_size: 1
eval_type: div2k-4
eval_bsize: 500

model_path: ./SoFoNO.pth

Demo

python demo.py --input input.png --model ./SoFoNO.pth --scale 2 --output output.png

Reference

• For PyTorch implementation details, see Ketkar et al., 2021.

Acknowledgements

This code is built on LIIF, LTE and SRNO

Bibtex citation

@article{oh2025sofono,
  title={SoFoNO: Arbitrary-scale image super-resolution via Sobolev Fourier neural operator},
  author={Oh, Jong Kwon and Son, Hwijae and Hwang, Hyung Ju and Oh, Jihyong},
  journal={Neurocomputing},
  pages={131944},
  year={2025},
  publisher={Elsevier}
}