FourierMamba：面向图像去雨的傅里叶学习与状态空间模型集成
FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining
AI总结：
本文提出FourierMamba框架，首次将Mamba引入傅里叶空间，通过空间维度的锯齿形扫描编码和通道维度的直接Mamba关联来建模不同频率间的依赖关系，从而提升图像去雨性能。
摘要：
图像去雨旨在从有雨图像中去除雨纹并恢复清晰背景。目前，一些采用傅里叶变换的研究已被证明对图像去雨有效，因为它可以作为捕获雨纹的有效频率先验。然而，尽管图像中存在低频和高频之间的依赖关系，这些基于傅里叶的方法很少利用不同频率之间的相关性来联合其学习过程，限制了频率信息在图像去雨中的充分利用。另一方面，最近出现的Mamba技术在建模各种域（例如空间、时间）中的相关性方面展现了有效性和高效性，我们认为将Mamba引入其尚未探索的傅里叶空间以关联不同频率将有助于改善图像去雨。这促使我们提出了一个名为FourierMamba的新框架，该框架在傅里叶空间中使用Mamba执行图像去雨。由于傅里叶空间中频率阶数的独特排列，FourierMamba的核心在于不同频率的扫描编码，其中低-高频阶数格式在空间维度（未按轴排列）和通道维度（按轴排列）中表现不同。因此，我们设计了FourierMamba，以不同的设计关联空间维度和通道维度中的傅里叶空间信息。具体而言，在空间维度的傅里叶空间中，我们引入锯齿形编码来扫描频率，以将阶数从低频到高频重新排列，从而有序地关联频率之间的连接；在通道维度的傅里叶空间中，频率阶数已按轴排列，我们可以直接使用Mamba执行频率关联并改善通道信息表示。
英文摘要：
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.
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