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FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining
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Proposes FourierMamba, a Mamba-based image deraining network that applies state space scanning in Fourier space, using zigzag-style scanning for spatial frequencies and channel-wise Fourier scanning for channel frequencies.
Problem
Image deraining methods using Fourier transforms rarely model correlations between low and high frequencies, limiting use of frequency information for removing rain streaks.
Approach
Introduces Mamba into Fourier space: a bilateral and progressive zigzag scan orders spatial-frequency coefficients from low to high frequency, and channel-dimension Fourier transform followed by Mamba scanning correlates channel frequencies; both combined in Fourier Residual State-Space Blocks within a U-Net.
Key results
- FourierMamba reports 31.79 dB PSNR / 0.913 SSIM on Rain100H, versus 31.74 / 0.912 for the second-best FreqMamba.
- On Rain100L it reports 39.73 dB PSNR / 0.986 SSIM, versus 39.18 / 0.981 for FreqMamba.
- On Test1200 it reports 34.76 dB PSNR / 0.938 SSIM; on Test2800 it reaches 34.23 dB, slightly below FreqMamba's 34.25 dB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the FSI-SSM Mamba scan with 1×1 convolution (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 39.05 | Hurt |
| replace the FSI-SSM Mamba scan with 1×1 convolution (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9835 | Hurt |
| replace the FCE-SSM Mamba scan with 1×1 convolution (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 39.08 | Hurt |
| replace the FCE-SSM Mamba scan with 1×1 convolution (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9836 | Hurt |
| remove the spatial-dimension Fourier transform (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 38.25 | Hurt |
| remove the spatial-dimension Fourier transform (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9810 | Hurt |
| remove the channel-dimension Fourier transform (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 38.72 | Hurt |
| remove the channel-dimension Fourier transform (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9827 | Hurt |
| use classic 2D scanning instead of combining the proposed Fourier-space scans (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 38.82 | Hurt |
| use classic 2D scanning instead of combining the proposed Fourier-space scans (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9817 | Hurt |
| use bilateral zigzag scanning alone instead of combining the proposed scans (ablation) | FourierMamba · Rain100L | PSNR: 39.73 -> 39.31 | Hurt |
| use bilateral zigzag scanning alone instead of combining the proposed scans (ablation) | FourierMamba · Rain100L | SSIM: 0.9856 -> 0.9844 | Hurt |
Surprising findings
- On Test2800, FourierMamba (34.23 dB) is slightly below FreqMamba (34.25 dB) in PSNR, despite the paper claiming best results across all datasets.
Limitations
- The paper states results are best on all datasets, but the table shows FreqMamba slightly higher on Test2800 PSNR and SSIM.
- Ablation is run only on Rain100L, with scanning comparisons limited to the spatial dimension.
Experimental setup
Datasets: Rain13k
Benchmarks: Rain100H Rain100L Test2800 Test1200
Metrics: PSNR SSIM
Baselines: DerainNet UMRL RESCAN PreNet MSPFN SPAIR MPRNet Restormer Fourmer IR-SDE MambaIR VMambaIR
Builds on: Mamba VMamba MambaIR Fourmer FreqMamba
Closest papers by meaning
- FMRNet: Image Deraining via Frequency Mutual Revision (AAAI 2024 · similarity 0.89)
- Beyond Spatial Domain: Cross-domain Promoted Fourier Convolution Helps Single Image Dehazing (AAAI 2025 · similarity 0.86)
- Bidirectional Multi-Scale Implicit Neural Representations for Image Deraining (CVPR 2024 · similarity 0.86)
- Rethinking Multi-Scale Representations in Deep Deraining Transformer (AAAI 2024 · similarity 0.85)
- Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting (NeurIPS 2024 · similarity 0.85)
- DiMSUM: Diffusion Mamba - A Scalable and Unified Spatial-Frequency Method for Image Generation (NeurIPS 2024 · similarity 0.85)
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