SA-ISAR Autofocusing and Cross-Range Scaling via Cross-Term-Aware Centroid Frequency-Chirp Rate Distribution Reconstruction

Inverse synthetic aperture radar (ISAR) provides an effective means for noncooperative target observation through high-resolution imaging; nevertheless, sparse aperture ISAR (SA-ISAR) autofocusing and cross-range scaling (CRS) for targets with spatial-variant Doppler remain challenging because incomplete observations and spatial-variant phase errors jointly degrade coherent integration. After translational motion compensation, this article exploits the centroid frequency–chirp rate (CFCR)-domain sparsity of the range-cell slow-time observations, which are characterized by a nonuniformly sampled multicomponent linear frequency-modulated (MCLFM) model. Accordingly, SA-ISAR autofocusing and CRS are cast as a CFCR-domain sparse reconstruction problem, for which this article proposes a Bayesian-covariance-aided pairwise-coupled Wiener reconstruction method for CFCR auto-terms, termed BPCW-ATR. A CFCR-domain sparse observation model based on instantaneous autocorrelation function (IAF) samples is first established, in which the desired auto-terms are linearized with respect to sparse CFCR-domain coefficients. In the proposed cross-term-aware Wiener framework, deterministic signal–signal cross-terms are parameterized by retained unordered CFCR-node pairs and incorporated into the observation covariance as structured interference, whereas the IAF-induced signal–noise cross-term and noise auto-term are modeled as stochastic disturbances whose covariance is adaptively inferred. Furthermore, to enable efficient CFCR-domain reconstruction, a structured two-dimensional preconditioned conjugate gradient (2D-PCG) solver is developed. The reconstructed CFCR auto-terms are then used for focused ISAR image formation, effective rotational velocity estimation, and CRS. Experiments on simulated and measured data demonstrate that BPCW-ATR enables reliable CFCR-domain reconstruction and achieves robust SA-ISAR autofocusing and CRS under high missing rates and low signal-to-noise ratios.