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

Dong Li, Yidi Liu, Xueyang Fu, Jie Huang, Senyan Xu, Qi Zhu, Zheng-Jun Zha
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:35342-35365, 2025.

Abstract

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. Owing 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. Extensive experiments reveal that our method outperforms state-of-the-art methods both qualitatively and quantitatively.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-li25be, title = {{F}ourier{M}amba: {F}ourier Learning Integration with State Space Models for Image Deraining}, author = {Li, Dong and Liu, Yidi and Fu, Xueyang and Huang, Jie and Xu, Senyan and Zhu, Qi and Zha, Zheng-Jun}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {35342--35365}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/li25be/li25be.pdf}, url = {https://proceedings.mlr.press/v267/li25be.html}, abstract = {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. Owing 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. Extensive experiments reveal that our method outperforms state-of-the-art methods both qualitatively and quantitatively.} }
Endnote
%0 Conference Paper %T FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining %A Dong Li %A Yidi Liu %A Xueyang Fu %A Jie Huang %A Senyan Xu %A Qi Zhu %A Zheng-Jun Zha %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-li25be %I PMLR %P 35342--35365 %U https://proceedings.mlr.press/v267/li25be.html %V 267 %X 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. Owing 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. Extensive experiments reveal that our method outperforms state-of-the-art methods both qualitatively and quantitatively.
APA
Li, D., Liu, Y., Fu, X., Huang, J., Xu, S., Zhu, Q. & Zha, Z.. (2025). FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:35342-35365 Available from https://proceedings.mlr.press/v267/li25be.html.

Related Material