DeRainMamba: Frequency-Aware Image Deraining

• DeRainMamba is a frequency-aware state space model that integrates Fourier-domain analysis and spatial enhancement to effectively remove rain streaks while preserving image textures.
• Its innovative FASSM module uses FFT to separate amplitude and phase for precise rain detection, while MDPConv gathers multi-directional gradients to restore local details.
• Empirical benchmarks show that DeRainMamba improves PSNR and SSIM with lower parameters and computational costs compared to traditional CNN, transformer, and prior SSM models.

DeRainMamba is a frequency-aware state space model designed for single image deraining. By integrating frequency-domain discrimination with multi-directional spatial enhancement within a unified U-Net architecture, DeRainMamba addresses the shortcomings of prior CNN and SSM models, yielding substantial improvements in both rain streak removal and detail preservation. The framework is characterized by its Frequency-Aware State-Space Module (FASSM) and Multi-Directional Perception Convolution (MDPConv), enabling accurate rain detection in the frequency domain and robust local structure recovery in the spatial domain. Extensive empirical studies indicate that DeRainMamba outperforms existing state-of-the-art methods in terms of both restoration quality and computational efficiency (Zhu et al., 8 Oct 2025).

1. Motivation and Theoretical Foundation

DeRainMamba was developed to reconcile the global context modeling strengths of long-sequence models with the sensitivity to fine local details. Conventional CNN-based derainers possess limited receptive fields, impeding global artifact removal. Transformer-based frameworks improve context modeling but incur high computational cost for large images. Prior state space models in the Mamba family achieve efficient sequence modeling but lack frequency-domain awareness, hampering discrimination between rain streaks and natural image details. Rain artifacts manifest predominantly in mid- and high-frequency bands; thus, effective deraining requires both global frequency analysis and fine spatial enhancement.

2. Frequency-Aware State-Space Module (FASSM)

FASSM is central to DeRainMamba’s ability to discern rain streaks without sacrificing image detail:

• The input feature $F_{in}$ is first normalized using Layer Normalization (LN).
• Two parallel branches operate:
  • Vision State Space Module (VSSM): Provides global spatial modeling within the state-space framework.
  • Residual Fourier Module (RFM): Projects $F_{in}$ to the frequency domain via FFT, processes amplitude $\mathcal{A}(X)$ and phase $\mathcal{P}(X)$ separately, then reconstructs the feature via inverse FFT and $1\times1$ convolution.
• The final output combines three terms:

  $$F_{out} = \text{VSSM}(\text{LN}(F_{in})) + \text{RFM}(F_{in}) + s \cdot F_{in}$$

  where $s$ is a learnable blending scalar.

• Fourier processing specifically:

  • Amplitude and phase are extracted:

    $$\mathcal{A}(X) = |\mathcal{V}(F(X))|, \qquad \mathcal{P}(X) = \angle \mathcal{V}(F(X))$$

  • Enhanced representation:

    $$\hat{H}(X) = \text{ReLU}(\text{Conv}_{1\times1}(\mathcal{A}(X)) + \text{Conv}_{1\times1}(\mathcal{P}(X)))$$

    $$X_{out} = \text{Conv}_{1\times1}(\mathcal{V}^{-1}(\hat{H}(X))) + \text{DWConv}(X)$$

  where $\text{DWConv}$ is a $3\times3$ depthwise convolution.

This strategy efficiently highlights the spectral signatures of rain, enabling aggressive suppression without loss of texture.

3. Multi-Directional Perception Convolution (MDPConv)

MDPConv restores local structure by explicit gradient-based feature extraction from multiple orientations:

• Five differential convolution branches (horizontal, vertical, angular, central difference, and vanilla convolution) derive directional gradient maps, facilitating the isolation of rain streaks from edges and contours.
• For scalability and inference efficiency, a re-parameterization merges these kernels so that at deployment only a single “equivalent kernel” ($K_{eq}$) is needed:

  $$F_{out} = \text{MDPConv}(F_{in}) = \sum_{i=1}^5 F_{in} \ast K_i = F_{in} \ast (\sum_{i=1}^5 K_i) = F_{in} \ast K_{eq}$$

This design maintains directional sensitivity while minimizing inference cost, lending superior edge preservation and artifact rejection.

4. Experimental Performance and Benchmarks

DeRainMamba was extensively validated on Rain200L, Rain200H, DID-Data, and DDN-Data using PSNR and SSIM:

Benchmark	DeRainMamba PSNR	SOTA Comparator	ΔPSNR	DeRainMamba SSIM	SOTA Comparator	ΔSSIM
Rain200H	36.71	DRSformer: 36.26	+0.45	0.9833	DRSformer:0.9765	+0.0068
DID-Data	32.84	MambaIR: 32.61	+0.23	0.9641	MambaIR:0.9607	+0.0034

Quantitative improvement over previous models is accompanied by qualitative evidence: DeRainMamba consistently removed pronounced rain streaks and preserved fine texture and natural color fidelity.

5. Computational Efficiency

DeRainMamba achieves high performance with only 27.8 million parameters—substantially lower than models such as Uformer ($\sim$50.9M) and MambaIR ($\sim$31.5M):

• Parameter reduction arises from the integration of efficient state-space modeling and re-parameterized MDPConv.
• Inference acceleration is obtained by fusing multi-branch convolutions into a single kernel, eliminating computational redundancy.
• This enables deployment in resource-constrained or real-time scenarios, extending practical utility beyond research-grade settings.

6. Practical Implications and Future Directions

The presented frequency-aware, detail-enhancing architecture demonstrates that simultaneous modeling of global spectral context and local spatial details yields superior deraining, especially visible under challenging benchmark conditions. While DeRainMamba raises state-of-the-art performance under standard conditions, unresolved challenges remain for extreme rain scenarios and complex degradations. Future work suggested includes generalization improvements—potentially via more advanced frequency-spatial fusions—and expanding robustness to more diverse environmental corruptions.

7. Context and Significance

DeRainMamba exemplifies the trend of hybrid state-space and frequency-domain modeling in low-level vision restoration. The balancing of Fourier-based discrimination with anisotropic spatial enhancement provides a unified framework that addresses the limitations of pure CNN or transformer/SSM architectures (Zhu et al., 8 Oct 2025). Its design underscores the value of detail-preserving priors and adaptive frequency-aware processing in achieving high-quality restoration within efficient, scalable networks.