Distributed through-the-wall radar imaging algorithm based on low-rank and sparsity constraints

When using distributed through-the-wall radar for detecting obscured targets, the system needs to address the interference caused by wall clutter. However, existing distributed through-the-wall radar imaging algorithms based on compressive sensing (CS) often assume that wall clutter has already been removed, or adopt a two-stage approach where existing wall clutter suppression algorithms are applied before obtaining the target image. To address this problem, this paper proposes a distributed through-the-wall radar imaging algorithm based on low-rank and sparsity constraints, which can simultaneously achieve wall clutter suppression and high-precision target imaging, aiming to solve issues such as long imaging times and wall clutter interference in distributed through-the-wall radar imaging based on CS. Specifically, the proposed algorithm first formulates an optimization problem by leveraging the low-rank nature of wall echoes, the sparsity of the target image, and the structural correlation of the target across different views. Then, a proximal gradient iterative algorithm is employed to efficiently solve the optimization problem, and the concept of the imaging support set is introduced to significantly improve the efficiency of the proposed algorithm. Simulations and real-world experiments validate the effectiveness of the proposed algorithm, offering a new approach for through-the-wall radar imaging.