Multi-Target ISAR Imaging of UAV Swarms Using Fast Reweighted Atomic Norm Denoising

Inverse Synthetic Aperture Radar (ISAR) imaging of UAV swarms presents significant challenges due to the coherent superposition of backscattered signals from multiple closely spaced targets. This work explores the extension of the Fast Reweighted Atomic Norm Denoising (FRAND) algorithm to this multi-target scenario. We develop a comprehensive mathematical framework that reformulates the atomic norm minimization problem for swarm imaging, incorporating weighted regularization and efficient optimization via the Two-Dimensional Alternating Direction Method of Multipliers (2D-ADMM). The proposed method handles both sparse aperture conditions and additive white Gaussian noise while maintaining computational efficiency. We simulate an ISAR system receiving composite echoes from UAV swarms, each modeled with distinct scattering centers. The results demonstrate that FRAND effectively disentangles the mixed signals and generates high-resolution range-Doppler profiles for individual UAVs, outperforming traditional methods like Multiple Signal Classification (MUSIC) and Cadzow in low Signal-to-Noise Ratio (SNR) conditions. Quantitative evaluation using Mean-Square Error (MSE) criteria confirms the superiority of the proposed approach. This study establishes the strong potential of atomic norm minimization for complex multi-target radar imaging applications.