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

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.

Learning and Generalizing Motion Primitives from Driving Data for Path-Tracking Applications

Considering the driving habits which are learned from the naturalistic driving data in the path-tracking system can significantly improve the acceptance of intelligent vehicles. Therefore, the goal of this paper is to generate the prediction results of lateral commands with confidence regions according to the reference based on the learned motion primitives. We present a two-level structure for learning and generalizing motion primitives through demonstrations. The lower-level motion primitives are generated under the path segmentation and clustering layer in the upper-level. The Gaussian Mixture Model(GMM) is utilized to represent the primitives and Gaussian Mixture Regression (GMR) is selected to generalize the motion primitives. We show how the upper-level can help to improve the prediction accuracy and evaluate the influence of different time scales and the number of Gaussian components. The model is trained and validated by using the driving data collected from the Beijing Institute of Technology (BIT) intelligent vehicle platform. Experiment results show that the proposed method can extract the motion primitives from the driving data and predict the future lateral control commands with high accuracy.