Hyper-ISTA-GHD: An Adaptive Hyperparameter Selection Framework for Highly Squinted Mode Sparse SAR Imaging

The highly squinted mode, as an operational configuration of synthetic aperture radar (SAR), fulfills specific remote sensing demands. Under equivalent conditions, it necessitates a higher pulse repetition frequency (PRF) than the side-looking mode but produces inferior imaging quality, thereby constraining its widespread application. By applying the sparse SAR imaging method to highly squinted SAR systems, imaging quality can be enhanced while simultaneously reducing PRF requirements and expanding swath. Hyperparameters in sparse SAR imaging critically influence reconstruction quality and computational efficiency, making hyperparameter optimization (HPO) a persistent research focus. Inspired by HPO techniques in the deep unfolding network (DUN), we modified the iterative soft-thresholding algorithm (ISTA) employed in fast sparse SAR reconstruction based on approximate observation operators. Our adaptation enables adaptive regularization parameter tuning during iterations while accelerating convergence. To improve the robustness of this enhanced algorithm under realistic SAR echoes with noise, we integrated hypergradient descent (HD) to automatically adjust the ISTA step size after regularization parameter convergence, thereby mitigating overfitting. The proposed method, named Hyper-ISTA-GHD, adaptively selects regularization parameters and step sizes. It achieves high-precision, rapid imaging for highly squinted SAR. Owing to its training-free iterative minimization framework, this approach exhibits superior generalization capabilities compared to existing DUN methods and demonstrates broad applicability across diverse SAR imaging modes and scene characteristics. Simulations show that the hyperparameter selection and reconstruction results of the proposed method are almost consistent with the optimal values of traditional methods under different signal-to-noise ratios and sampling rates, but the time consumption is only one-tenth of that of traditional methods. Comparative experiments on the generalization performance with DUN show that the generalization performance of the proposed method is significantly better than DUN in extremely sparse scenarios.