Azimuth-Frequency Conditioned Mamba U-Net for ISAR Image Refocusing

High-order phase defocus occurs in ISAR imaging of maneuvering targets. Traditional methods are limited by motion model mismatches, whereas existing deep imaging relies on complex-valued convolutions or self-attention mechanisms, whose excessive computational complexity hinders real-time processing. To address these issues, this paper proposes an Azimuth-Frequency Conditioned Mamba U-Net (AFC-Mamba U-Net) for ISAR image refocusing. The method treats the real and imaginary parts of the defocused complex image as dual-channel real-valued inputs, integrating linear-complexity state-space modeling with cross-layer feature fusion to significantly reduce computational and memory overhead while maintaining high refocusing quality. Specifically, we design an Azimuth-Frequency Conditional Mamba block (AFCMambaBlock), which performs bidirectional selective state-space scanning along the azimuth axis to capture long-range defocus dependencies with linear time complexity, and introduces azimuth-frequency conditional gating to incorporate frequency-domain phase error information into spatial features. A phase-state bottleneck is constructed to aggregate multi-scale enhanced states via a cross-scale state bank, forming globally phase-error-aware representations. Furthermore, we propose a state-guided skip connection mechanism that dynamically gates encoder skip features using bottleneck states, effectively suppressing the propagation of defocus artifacts while reducing redundant computations in the decoder. Experiments conducted on a simulated dataset containing eight types of spaceborne targets and real-world Yak-42 aircraft data demonstrate that the proposed method reduces MSE by 35.8% and NMSE by 41.5% compared to CNN-based U-Net, while achieving an SSIM of 0.9901. Compared to the state-of-the-art complex-domain network CVPHD, the proposed method achieves a significantly better efficiency-accuracy trade-off: it reduces model parameters and computational complexity by approximately two orders of magnitude, improves inference speed by more than fivefold, and cuts GPU memory usage by about 96%, while maintaining competitive structural consistency (SSIM > 0.99). Although CVPHD retains better MSE and NMSE on simulated data, the proposed method provides a lightweight and feasible solution for real-time and embedded ISAR refocusing.