  In recent years, State Space Models (SSMs) with efficient hardware-aware
designs, known as the Mamba deep learning models, have made significant
progress in modeling long sequences such as language understanding. Therefore,
building efficient and general-purpose visual backbones based on SSMs is a
promising direction. Compared to traditional convolutional neural networks
(CNNs) and Vision Transformers (ViTs), the performance of Vision Mamba (ViM)
methods is not yet fully competitive. To enable SSMs to process image data,
ViMs typically flatten 2D images into 1D sequences, inevitably ignoring some 2D
local dependencies, thereby weakening the model's ability to interpret spatial
relationships from a global perspective. We use Fast Fourier Transform (FFT) to
obtain the spectrum of the feature map and add it to the original feature map,
enabling ViM to model a unified visual representation in both frequency and
spatial domains. The introduction of frequency domain information enables ViM
to have a global receptive field during scanning. We propose a novel model
called Vim-F, which employs pure Mamba encoders and scans in both the frequency
and spatial domains. Moreover, we question the necessity of position embedding
in ViM and remove it accordingly in Vim-F, which helps to fully utilize the
efficient long-sequence modeling capability of ViM. Finally, we redesign a
patch embedding for Vim-F, leveraging a convolutional stem to capture more
local correlations, further improving the performance of Vim-F. Code is
available at: \url{https://github.com/yws-wxs/Vim-F}.
