# FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining

arXiv: https://arxiv.org/abs/2405.19450 · HTML: https://mlsanity.com/paper/2405.19450/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Placed in Mamba for image restoration, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 29 May 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Mamba for image restoration](https://mlsanity.com/ssm/mamba-for-image-restoration/)

## Builds on (most cited first, 29 of 29)

- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Progressive Image Deraining Networks: A Better and Simpler Baseline](https://mlsanity.com/paper/1901.09221/) (2019)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [Multi-Scale Progressive Fusion Network for Single Image Deraining](https://mlsanity.com/paper/2003.10985/) (2020)
- [Density-aware Single Image De-raining using a Multi-stream Dense Network](https://mlsanity.com/paper/1802.07412/) (2018)
- [TransWeather: Transformer-based Restoration of Images Degraded by Adverse Weather Conditions](https://mlsanity.com/paper/2111.14813/) (2021)
- [HINet: Half Instance Normalization Network for Image Restoration](https://mlsanity.com/paper/2105.06086/) (2021)
- [Recurrent Squeeze-and-Excitation Context Aggregation Net for Single Image Deraining](https://mlsanity.com/paper/1807.05698/) (2018)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Clearing the Skies: A deep network architecture for single-image rain removal](https://mlsanity.com/paper/1609.02087/) (2016)
- [Uncertainty Guided Multi-Scale Residual Learning-using a Cycle Spinning CNN for Single Image De-Raining](https://mlsanity.com/paper/1906.11129/) (2019)
- [VmambaIR: Visual State Space Model for Image Restoration](https://mlsanity.com/paper/2403.11423/) (2024)
- [Embedding Fourier for Ultra-High-Definition Low-Light Image Enhancement](https://mlsanity.com/paper/2302.11831/) (2023)
- [Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Models](https://mlsanity.com/paper/2304.08291/) (2023)
- [Intriguing Findings of Frequency Selection for Image Deblurring](https://mlsanity.com/paper/2111.11745/) (2021)
- [Spatially-Adaptive Image Restoration using Distortion-Guided Networks](https://mlsanity.com/paper/2108.08617/) (2021)
- [Fourier Space Losses for Efficient Perceptual Image Super-Resolution](https://mlsanity.com/paper/2106.00783/) (2021)
- [MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection](https://mlsanity.com/paper/2403.19888/) (2024)
- [Online-updated High-order Collaborative Networks for Single Image Deraining](https://mlsanity.com/paper/2202.06568/) (2022)

## Built on by (most cited first, 30 of 33)

- [Directing Mamba to Complex Textures: An Efficient Texture-Aware State Space Model for Image Restoration](https://mlsanity.com/paper/2501.16583/) (2025)
- [QMambaBSR: Burst Image Super-Resolution with Query State Space Model](https://mlsanity.com/paper/2408.08665/) (2024)
- [Mamba in Vision: A Comprehensive Survey of Techniques and Applications](https://mlsanity.com/paper/2410.03105/) (2024)
- [TinyViM: Frequency Decoupling for Tiny Hybrid Vision Mamba](https://mlsanity.com/paper/2411.17473/) (2024)
- [Integrating Extra Modality Helps Segmentor Find Camouflaged Objects Well](https://mlsanity.com/paper/2502.14471/) (2025)
- [S3Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model](https://mlsanity.com/paper/2411.11906/) (2024)
- [Semi-Supervised State-Space Model with Dynamic Stacking Filter for Real-World Video Deraining](https://mlsanity.com/paper/2505.16811/) (2025)
- [Scan Clusters, Not Pixels: A Cluster-Centric Paradigm for Efficient Ultra-high-definition Image Restoration](https://mlsanity.com/paper/2602.21917/) (2026)
- [A Hybrid Transformer-Mamba Network for Single Image Deraining](https://mlsanity.com/paper/2409.00410/) (2024)
- [MODEM: A Morton-Order Degradation Estimation Mechanism for Adverse Weather Image Recovery](https://mlsanity.com/paper/2505.17581/) (2025)
- [PRE-Mamba: A 4D State Space Model for Ultra-High-Frequent Event Camera Deraining](https://mlsanity.com/paper/2505.05307/) (2025)
- [TPGDiff: Hierarchical Triple-Prior Guided Diffusion for Image Restoration](https://mlsanity.com/paper/2601.20306/) (2026)
- [Alignment-free Raw Video Demoireing](https://mlsanity.com/paper/2408.10679/) (2024)
- [OSMamba: Omnidirectional Spectral Mamba with Dual-Domain Prior Generator for Exposure Correction](https://mlsanity.com/paper/2411.15255/) (2024)
- [FTMoMamba: Motion Generation with Frequency and Text State Space Models](https://mlsanity.com/paper/2411.17532/) (2024)
- [Uncovering the Spectral Bias in Diagonal State Space Models](https://mlsanity.com/paper/2508.20441/) (2025)
- [CompEvent: Complex-valued Event-RGB Fusion for Low-light Video Enhancement and Deblurring](https://mlsanity.com/paper/2511.14469/) (2025)
- [EventGait: Towards Robust Gait Recognition with Event Streams](https://mlsanity.com/paper/2605.22139/) (2026)
- [Event-Illumination Collaborative Low-light Image Enhancement with a High-resolution Real-world Dataset](https://mlsanity.com/paper/2605.22186/) (2026)
- [Venturing into Uncharted Waters: The Navigation Compass from Transformer to Mamba](https://mlsanity.com/paper/2406.16722/) (2024)
- [DeshadowMamba: Deshadowing as 1D Sequential Similarity](https://mlsanity.com/paper/2510.24260/) (2025)
- [M3SR: Multi-Scale Multi-Perceptual Mamba for Efficient Spectral Reconstruction](https://mlsanity.com/paper/2601.08293/) (2026)
- [FourierPET: Deep Fourier-based Unrolled Network for Low-count PET Reconstruction](https://mlsanity.com/paper/2601.11680/) (2026)
- [Derain-Agent: A Plug-and-Play Agent Framework for Rainy Image Restoration](https://mlsanity.com/paper/2603.11866/) (2026)
- [Pixel Ignores, Superpixel Sees: Adverse Weather Image Restoration via Semantic-Center SSM](https://mlsanity.com/paper/2608.01760/) (2026)
- [DeRainMamba: A Frequency-Aware State Space Model with Detail Enhancement for Image Deraining](https://mlsanity.com/paper/2510.06746/) (2025)
- [Semantics and Content Matter: Towards Multi-Prior Hierarchical Mamba for Image Deraining](https://mlsanity.com/paper/2511.13113/) (2025)
- [DeepRFTv2: Kernel-level Learning for Image Deblurring](https://mlsanity.com/paper/2511.21132/) (2025)
- [WaterWave: Bridging Underwater Image Enhancement into Video Streams via Wavelet-based Temporal Consistency Field](https://mlsanity.com/paper/2512.05492/) (2025)
- [PAS-Mamba: Phase-Amplitude-Spatial State Space Model for MRI Reconstruction](https://mlsanity.com/paper/2601.14530/) (2026)

## Abstract (arXiv)

Image deraining aims to remove rain streaks from rainy images and restore clear backgrounds. Currently, some research that employs the Fourier transform has proved to be effective for image deraining, due to it acting as an effective frequency prior for capturing rain streaks. However, despite there exists dependency of low frequency and high frequency in images, these Fourier-based methods rarely exploit the correlation of different frequencies for conjuncting their learning procedures, limiting the full utilization of frequency information for image deraining. Alternatively, the recently emerged Mamba technique depicts its effectiveness and efficiency for modeling correlation in various domains (e.g., spatial, temporal), and we argue that introducing Mamba into its unexplored Fourier spaces to correlate different frequencies would help improve image deraining. This motivates us to propose a new framework termed FourierMamba, which performs image deraining with Mamba in the Fourier space. Owning to the unique arrangement of frequency orders in Fourier space, the core of FourierMamba lies in the scanning encoding of different frequencies, where the low-high frequency order formats exhibit differently in the spatial dimension (unarranged in axis) and channel dimension (arranged in axis). Therefore, we design FourierMamba that correlates Fourier space information in the spatial and channel dimensions with distinct designs. Specifically, in the spatial dimension Fourier space, we introduce the zigzag coding to scan the frequencies to rearrange the orders from low to high frequencies, thereby orderly correlating the connections between frequencies; in the channel dimension Fourier space with arranged orders of frequencies in axis, we can directly use Mamba to perform frequency correlation and improve the channel information representation.