Non-Convex Joint Sparse and Low-Rank Optimization for Enhanced ISAR Imaging from Incomplete Data

Conventional inverse synthetic aperture radar (ISAR) imaging techniques can produce high-resolution imagery from complete observation data. However, in practical scenarios, incomplete data caused by undersampling or missing data often leads to defocused results with traditional methods. While compressive sensing or low-rank reconstruction approaches have been proposed to address this challenge, existing techniques frequently fail to fully exploit both the sparsity and low-rank properties inherent in ISAR scenes. Moreover, they typically rely on convex approximations that introduce estimation bias, weaken sparsity promotion, and increase computational complexity, ultimately degrading imaging performance. To overcome these limitations, this work presents an enhanced sparse ISAR imaging method that jointly enforces non-convex sparsity and low-rank constraints for incomplete data recovery. The imaging model incorporates both inherent sparsity priors and a low-rank constraint. The resulting non-convex optimization problem is solved via an efficient iterative algorithm based on the alternating direction method of multipliers, where the sparse component is reconstructed using an iterative reweighted scheme with a regularizer and the low-rank component is recovered through truncated singular value decomposition. Experimental results on both simulated and measured data demonstrate the efficacy and superior performance of the proposed method.