Complex Primal–Dual Network for Sparse Aperture Inverse Synthetic Aperture LiDAR Imaging

Inverse synthetic aperture lidar (ISAL) is a radar system that combines synthetic aperture imaging and laser technology. However, due to high cross-range repetition frequency of the laser band, system complexity, and data redundancy, the echo signals of ISAL are usually nonuniform and incomplete. These data are called sparse aperture (SA) data, which lead to defocusing in ISAL images, and traditional imaging algorithms have limited capability to reconstruct target details under SA conditions. To address this problem, we propose a new framework called complex-valued primal-dual network (CPD-Net). Specifically, we unroll the iterations of the primal-dual hybrid gradient algorithm to a learnable deep network architecture, and gradually relax the constraints to reconstruct ISAL images from highly undersampled range profiles. To enable ISAL to image targets at different scales, we designed a complex-valued fusion inception module (CFIM) based on the Inception structure and convolutional neural networks. The Inception layers in CFIM employ multiple convolutional layers with different kernel sizes in parallel. The feature matrices obtained from different convolutional operations are concatenated along the depth dimension to form a deeper matrix, thereby enhancing the feature extraction capability of CPD-Net. In addition, the CPD-Net employs complex-valued operations to process the phase information of laser signals, and incorporates residual connections to improve CPD-Net’s performance. Experiments on simulated data and measured data demonstrate that CPD-Net can obtain well-focused ISAL images with clear backgrounds under different signal-to-noise ratios (SNRs) and SA types. Moreover, compared with traditional optimization algorithms, CPD-Net significantly reduces computational time, making it more practical for real ISAL applications.