# Domain Generalization with Fourier Transform and Soft Thresholding

arXiv: https://arxiv.org/abs/2309.09866 · HTML: https://mlsanity.com/paper/2309.09866/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [FedDG: Federated Domain Generalization on Medical Image Segmentation via Episodic Learning in Continuous Frequency Space](https://mlsanity.com/paper/2103.06030/) (2021)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [REFUGE Challenge: A Unified Framework for Evaluating Automated Methods for Glaucoma Assessment from Fundus Photographs](https://mlsanity.com/paper/1910.03667/) (2019)
- [DoFE: Domain-oriented Feature Embedding for Generalizable Fundus Image Segmentation on Unseen Datasets](https://mlsanity.com/paper/2010.06208/) (2020)
- [Gradual Fine-Tuning for Low-Resource Domain Adaptation](https://mlsanity.com/paper/2103.02205/) (2021)
- [A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer](https://mlsanity.com/paper/2305.17510/) (2023)
- [Domain Generalization with Adversarial Intensity Attack for Medical Image Segmentation](https://mlsanity.com/paper/2304.02720/) (2023)
- [A Simulation Study to Evaluate the Performance of the Cauchy Proximal Operator in Despeckling SAR Images of the Sea Surface](https://mlsanity.com/paper/2012.06657/) (2020)
- [Real-time Wireless ECG-derived Respiration Rate Estimation Using an Autoencoder with a DCT Layer](https://mlsanity.com/paper/2211.08491/) (2022)

## Built on by (most cited first, 4 of 4)

- [Cyst-X: A Multi-Center MRI Benchmark and Federated Learning Framework for Malignancy-Risk Stratification of Pancreatic Cystic Neoplasm](https://mlsanity.com/paper/2507.22017/) (2025)
- [Towards Single-Source Domain Generalized Object Detection via Causal Visual Prompts](https://mlsanity.com/paper/2510.19487/) (2025)
- [Federated Breast Cancer Detection Enhanced by Synthetic Ultrasound Image Augmentation](https://mlsanity.com/paper/2506.23334/) (2025)
- [BreastMammo and DenseMammo: Benchmarks for Mammography Domain Generalization](https://mlsanity.com/paper/2608.10271/) (2026)

## Abstract (arXiv)

Domain generalization aims to train models on multiple source domains so that they can generalize well to unseen target domains. Among many domain generalization methods, Fourier-transform-based domain generalization methods have gained popularity primarily because they exploit the power of Fourier transformation to capture essential patterns and regularities in the data, making the model more robust to domain shifts. The mainstream Fourier-transform-based domain generalization swaps the Fourier amplitude spectrum while preserving the phase spectrum between the source and the target images. However, it neglects background interference in the amplitude spectrum. To overcome this limitation, we introduce a soft-thresholding function in the Fourier domain. We apply this newly designed algorithm to retinal fundus image segmentation, which is important for diagnosing ocular diseases but the neural network's performance can degrade across different sources due to domain shifts. The proposed technique basically enhances fundus image augmentation by eliminating small values in the Fourier domain and providing better generalization. The innovative nature of the soft thresholding fused with Fourier-transform-based domain generalization improves neural network models' performance by reducing the target images' background interference significantly. Experiments on public data validate our approach's effectiveness over conventional and state-of-the-art methods with superior segmentation metrics.