Computationally Efficient Short-Range 3D SAR Imaging via Modified Augmented Lagrangian-Based FA-ADMM and Deep Learning Models

Short-range three-dimensional (3D) synthetic aperture radar (SAR) imaging has drawn significant attention across various domains, including security surveillance, non-destructive testing, and medical diagnostics. This paper introduces a fast adaptive alternative direction method of multipliers (FA-ADMM) framework designed to enhance both efficiency and accuracy in SAR image reconstruction. Our approach addresses two key challenges in the single holographic frequency ADMM (SFH-ADMM) model: image degradation from fast Fourier transform operations and slow convergence due to fixed ADMM penalty parameters. To overcome these issues, we refine the augmented Lagrangian formulation to ensure stable convergence and introduce an adaptive tuning mechanism that dynamically adjusts penalty parameters based on the connection between relaxed ADMM and relaxed Douglas–Rachford splitting. Additionally, we seamlessly integrate denoising convolutional neural network and autoencoder architectures into the iterative process to enhance noise suppression and image fidelity, respectively. The synergy of these innovations within a unified framework significantly accelerates convergence and improves reconstruction quality, making it well suited for real-world short-range 3D SAR applications.