Sparse and Low-rank Decomposition of Hankel Matrix for SAR Imaging

Sparse Synthetic Aperture Radar (SAR) imaging based on compressive sensing allows radar systems to capture targets with sampling rates below the Nyquist limit by exploiting target sparsity. However, preserving the structural integrity of original data, particularly for periodic or correlated targets, remains a challenge. To address this, we propose a novel SAR imaging approach that incorporates prior target information using sparse and low-rank decomposition of Hankel matrices. Our method employs nuclear norm minimization with low-rank matrix factorization initialization to decompose these matrices, eliminating the need for explicit dictionary priors. By leveraging the duality between signal sparsity and low-rank structures, the method adapts to targets with complex or varying characteristics. Using alternating direction method of multipliers for reconstruction, the approach demonstrates superior performance in real SAR data.