Fast ISAR Imaging Algorithm for Azimuth Gapped Data Based on Structured Toeplitz Matrix

With the advancement of modern radar systems, there are increasingly stringent requirements for reconstructing Inverse Synthetic Aperture Radar (ISAR) images from gap missing sampling (GMS) data. Compressed sensing (CS), while being a conventional approach for sparse reconstruction, suffers from inherent discrete dictionary mismatch issues that degrade reconstruction accuracy. Matrix completion (MC) methods, leveraging the low-rank properties of matrices, prevent the grid mismatch problem by directly recovering missing data. Although existing Hankel transformation methods can address GMS reconstruction, their computational efficiency remains quite slow. To address the fast ISAR imaging problem with azimuth GMS, we propose a fast imaging algorithm based on structured Toeplitz matrix. Our approach leverages the inherent low-rank properties of data by employing a structured Toeplitz formulation, thereby exploiting the enhanced low-rank property from the data structure. Numerical simulations reveal that the Toeplitz transformation achieves superior accuracy relative to the Hankel transformation. For achieving high-efficiency and high-precision image reconstruction, we further develop a reconstruction algorithm based on the fast Alternating Direction Method of Multipliers (ADMM). In contrast to the SLR+S algorithm using Hankel transformation, our proposed algorithm significantly reduces computational time while maintaining reconstruction accuracy. Finally, the experimental results further validate the effectiveness of the proposed algorithm, providing substantial support for its engineering applications.