Efficient and Robust Sparse Aperture ISAR Imaging Based on Log-Sum Minimization

Inverse synthetic aperture radar (ISAR) imaging of sparse aperture is a challenging problem. Noting the ISAR image generally exhibits strong sparsity, compressive sensing (CS) and sparse signal recovery methods are widely applied for sparse aperture data. However, the existing sparse aperture ISAR imaging algorithms are either computationally heavy or require manual adjustment of too many parameters, which limits their applications in the real-time ISAR imaging system. This paper proposes a high precision and computationally efficient ISAR imaging algorithm for sparse aperture. A generalized CS model with log-sum minimization is first considered for ISAR imaging, and then the iterative log-sum thresholding (ILT) algorithm is utilized to solve the optimization problem, where no large-scale matrix inversion is performed for reducing the computational overhead. Specifically, to efficiently estimate ISAR image sparsity and avoid manually tuning parameters, a modified version of the ILT algorithm is proposed, in which an adjustment strategy of the trade-off parameter λ is adopted. To analyze the influence of different measurement matrix on the imaging algorithm, four sparse sampling patterns, including centralized sampling (CES), block centralized sampling (BCS), equally space sampling (ESS), and random sampling (RAS), are analyzed based on the mutual incoherence property (MIP). Experiments based on both simulated and measured data substantiate that the proposed two algorithms can achieve well-focused ISAR images and are very efficient to implement. In particular, the imaging time of the modified algorithm is less than one second for a matrix dimension of size 256 × 256, which meets the real-time requirements.