Cross-Range Super-Resolution ISAR Imaging Under Ultrashort Sparse Aperture: An Orthonormal Atomic Norm Approach

As state-of-the-art gridless sparse aperture inverse synthetic aperture radar (SA-ISAR) imaging methods, the atomic norm minimization (ANM)-based methods significantly enhance the quality of ISAR images by eliminating spurious scattering centers (SCs) caused by off-grid errors. However, on the one hand, these methods are severely limited by the minimum atomic separation constraint, making it difficult to resolve SCs at cross-range distances below the Rayleigh resolution. Additionally, this constraint required for reliable ANM recovery can be difficult to hold in practical ISAR imaging, leading to low-quality imaging results. This is primarily due to the effective rotation angle (ERA) available for ISAR imaging is usually small. On the other hand, existing algorithms for resolving ANM need to select crucial auxiliary parameters, which causes much inconvenience to SA-ISAR imaging applications. Aiming at these issues, we present a super-resolution SA-ISAR imaging framework based on orthonormal ANM (OANM). Due to the utilization of orthogonality, the framework is possible to operate independently of the minimum atomic separation constraint and is capable of resolving SCs regardless of how closely they are spaced. Furthermore, to avoid the need for selecting auxiliary parameters, we propose a novel OANM and Iterative Vandermonde Decomposition and Shrinkage-Threshold-Free (OANM-IVDSTF) algorithm within accelerated proximal gradient (APG) framework. By introducing a modified second-order statistic of eigenvalues (SORTE) strategy, the low-rank projection is completed adaptively during iterations, rather than relying on a fixed shrinkage-threshold parameter. Both the simulated and measured data results validate the effectiveness of the proposed method under conditions of SA with a small ERA.