F $^\mathbf {2}$ Mamba: Frequency-Aware and Flexibly-Unfolded Mamba for Compressed Sensing

Existing Deep Unfolding Networks (DUNs) typically employ a series of repeated network modules to unfold traditional algorithms for compressed sensing (CS), resulting in redundant feature information extracted at different iterative stages. Additionally, the neglect of frequency-domain information limits the feature extraction efficiency of DUNs. To address these issues, we propose a Flexibly-Unfolded and Frequency-Aware Mamba network for CS, called F $^{2}$ Mamba. Specifically, the proposed F $^{2}$ Mamba integrates a sequence of Flexible Unfolding Mamba Satge (FUMSs) for iterative image recovery. Each FUMS flexibly unfolds one iterative step of the homotopy algorithm through a tunable architecture comprising two L-Mamba and a Frequency Prior Extraction Block (FPEB), enabling the perception of image features at different scale space. The L-Mamba, primarily composed of cross Mamba blocks, establishes global receptive fields at multiple scales while enhancing local information perception through a cross mechanism. Meanwhile, the FPEB enhances the extraction of frequency-domain priors within the mathematical framework of homotopy algorithms. Finally, we introduce a hierarchical feature complementarity module to integrate shallow image patterns and deep semantic abstractions across the FUMSs, thereby obtaining the reconstructed image. Experimental results demonstrate that, compared to other state-of-the-art methods, our proposed F $^{2}$ Mamba achieves superior performance in image quality metrics, such as SSIM and PSNR, as well as in visual perception.