Under sparse aperture (SA) conditions, inverse synthetic aperture radar (ISAR) imaging becomes a severely ill-posed inverse problem due to undersampled and noisy measurements, leading to pronounced degradation in azimuth resolution and image quality. Although deep learning approaches have demonstrated promising performance for SA-ISAR imaging, their practical deployment is often hindered by black-box behavior, fixed network depth, high computational cost, and limited robustness under extreme operating conditions. To address these challenges, this paper proposes an ADMM Denoising Deep Equilibrium Framework (ADnDEQ) for SA-ISAR imaging. The proposed method reformulates an ADMM-based unfolding process as an implicit deep equilibrium (DEQ) model, where ADMM provides an interpretable optimization structure and a lightweight DnCNN is embedded as a learned proximal operator to enhance robustness against noise and sparse sampling. By representing the reconstruction process as the equilibrium solution of a single-layer network with shared parameters, ADnDEQ decouples forward and backward propagation, achieves constant memory complexity, and enables flexible control of inference iterations. Experimental results demonstrate that the proposed ADnDEQ framework achieves superior reconstruction quality and robustness compared with conventional layer-stacked networks, particularly under low sampling ratios and low-SNR conditions, while maintaining significantly reduced computational cost.
Song et al. (Mon,) studied this question.