mlsanityData to 14 Oct 2026

Deep Fourier Up-Sampling

arXiv 2210.05171 ↗First posted 11 Oct 2022cs.CVcited by 27

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Abstract (arXiv)

Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (e.g., interpolation, transposed convolution, and un-pooling) heavily depend on local pixel attention, incapably exploring the global dependency. In contrast, the Fourier domain obeys the nature of global modeling according to the spectral convolution theorem. Unlike the spatial domain that performs up-sampling with the property of local similarity, up-sampling in the Fourier domain is more challenging as it does not follow such a local property. In this study, we propose a theoretically sound Deep Fourier Up-Sampling (FourierUp) to solve these issues. We revisit the relationships between spatial and Fourier domains and reveal the transform rules on the features of different resolutions in the Fourier domain, which provide key insights for FourierUp's designs. FourierUp as a generic operator consists of three key components: 2D discrete Fourier transform, Fourier dimension increase rules, and 2D inverse Fourier transform, which can be directly integrated with existing networks. Extensive experiments across multiple computer vision tasks, including object detection, image segmentation, image de-raining, image dehazing, and guided image super-resolution, demonstrate the consistent performance gains obtained by introducing our FourierUp.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). Builds on 24 of its 55 references that are in the map. First posted on arXiv 11 Oct 2022.

Builds on

24 of 55 references.

References · 24

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2015Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networkscited by 9,639
  3. 2016Feature Pyramid Networks for Object Detectioncited by 5,036
  4. 2021TransUNet: Transformers Make Strong Encoders for Medical Image Segmentationcited by 1,558
  5. 2018Attention U-Net: Learning Where to Look for the Pancreascited by 1,435
  6. 2019EfficientDet: Scalable and Efficient Object Detectioncited by 1,020
  7. 2020FDA: Fourier Domain Adaptation for Semantic Segmentationcited by 541
  8. 2017Benchmarking Single Image Dehazing and Beyondcited by 447
  9. 2019Progressive Image Deraining Networks: A Better and Simpler Baselinecited by 272
  10. 2018Density-aware Single Image De-raining using a Multi-stream Dense Networkcited by 248
  11. 2020Multi-Scale Boosted Dehazing Network with Dense Feature Fusioncited by 230
  12. 2017Image De-raining Using a Conditional Generative Adversarial Networkcited by 197
12 more
  1. 2019Variational Denoising Network: Toward Blind Noise Modeling and Removalcited by 117
  2. 2015Spectral Representations for Convolutional Neural Networkscited by 81
  3. 2018Lightweight Pyramid Networks for Image Derainingcited by 64
  4. 2017CirCNN: Accelerating and Compressing Deep Neural Networks Using Block-CirculantWeight Matricescited by 55
  5. 2020Domain Adaptive Relational Reasoning for 3D Multi-Organ Segmentationcited by 48
  6. 2018Learning Dual Convolutional Neural Networks for Low-Level Visioncited by 35
  7. 2022Memory-augmented Deep Unfolding Network for Guided Image Super-resolutioncited by 25
  8. 2018Feature Pyramid Network for Multi-Class Land Segmentationcited by 24
  9. 2020Neural Sparse Representation for Image Restorationcited by 22
  10. 2018FALCON: A Fourier Transform Based Approach for Fast and Secure Convolutional Neural Network Predictionscited by 20
  11. 2019IPG-Net: Image Pyramid Guidance Network for Small Object Detectioncited by 10
  12. 2021Unfolding Taylor's Approximations for Image Restorationcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 15; 2024: 8; 2025: 3; 2026: 1.

27 papers.

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  1. 2023Equivariant Multi-Modality Image Fusioncited by 99
  2. 2023FourLLIE: Boosting Low-Light Image Enhancement by Fourier Frequency Informationcited by 64
  3. 2023Sparse Sampling Transformer with Uncertainty-Driven Ranking for Unified Removal of Raindrops and Rain Streakscited by 45
  4. 2023NightHazeFormer: Single Nighttime Haze Removal Using Prior Query Transformercited by 19
  5. 20243D-GSW: 3D Gaussian Splatting for Robust Watermarkingcited by 18
  6. 2023OPE-SR: Orthogonal Position Encoding for Designing a Parameter-free Upsampling Module in Arbitrary-scale Image Super-Resolutioncited by 17
  7. 2023FreMIM: Fourier Transform Meets Masked Image Modeling for Medical Image Segmentationcited by 11
  8. 2024Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolutioncited by 11
  9. 2023Hybrid Transformer and CNN Attention Network for Stereo Image Super-resolutioncited by 10
  10. 2024PPTFormer: Pseudo Multi-Perspective Transformer for UAV Segmentationcited by 10
  11. 2023OPDN: Omnidirectional Position-aware Deformable Network for Omnidirectional Image Super-Resolutioncited by 9
  12. 2024EmMixformer: Mix transformer for eye movement recognitioncited by 9
15 more
  1. 2023Resolution-Invariant Image Classification based on Fourier Neural Operatorscited by 7
  2. 2025Noise Matters: Optimizing Matching Noise for Diffusion Classifierscited by 7
  3. 2023Local-Global Transformer Enhanced Unfolding Network for Pan-sharpeningcited by 6
  4. 2024RSHazeDiff: A Unified Fourier-aware Diffusion Model for Remote Sensing Image Dehazingcited by 6
  5. 2023Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusioncited by 5
  6. 2023Pixel Adapter: A Graph-Based Post-Processing Approach for Scene Text Image Super-Resolutioncited by 5
  7. 2024I3Net: Inter-Intra-slice Interpolation Network for Medical Slice Synthesiscited by 5
  8. 2023Decomposition Ascribed Synergistic Learning for Unified Image Restorationcited by 3
  9. 2024MacFormer: Semantic Segmentation with Fine Object Boundariescited by 3
  10. 2023A Dual Domain Multi-exposure Image Fusion Network based on the Spatial-Frequency Integrationcited by 2
  11. 2023Enhancing Infrared Small Target Detection Robustness with Bi-Level Adversarial Frameworkcited by 1
  12. 2025UHKD: A Unified Framework for Heterogeneous Knowledge Distillation via Frequency-Domain Representationscited by 1
  13. 2024Textless NLP -- Zero Resource Challenge with Low Resource Computecited by 0
  14. 2025DeepRFTv2: Kernel-level Learning for Image Deblurringcited by 0
  15. 2026FSM-Net: An Efficient Frequency-Spatial Network for Real-World Deblurringcited by 0