Lightweight FISTA-Inspired Sparse Reconstruction Network for mmW 3-D Holography

Integrating compressed sensing (CS) with millimeter-wave (mmW) holography has shown great potential to achieve lightweight onboard hardware, low sampling ratio, and high-speed sensing. However, conventional CS-driven algorithms are always limited by nontrivial adjusting of parameters and excessive computational cost caused by plenty of iterations. To address this problem, we propose a lightweight model-based deep learning framework (LFIST-Net) for mmW 3-D holography, by combining the interpretability of fast iterative shrinkage-thresholding algorithm (FISTA) and tuning-free merit of data-driven deep neural network. First, the single-frequency (SF) holographic imaging technique is integrated into FISTA, which serves as the sensing kernels, to avoid large-scale matrix multiplications. Subsequently, the kernel-based FISTA (KFISTA) is mapped into layer-fixed and parameter-learnable LFIST-Net, whose weights are relaxed to be layer-varied. The updating of key parameters in LFIST-Net, including step sizes, thresholds, and momentum coefficients, are regularized by soft-plus function to ensure the non-negativity and monotonicity. As for 3-D holography implementation, the “1-D + 2-D” scheme is adopted, where the matched filtering (MF) and well-trained LFIST-Net are used for range focusing and reconstructions of azimuth slices. Without losing efficiency, the range-focused subechoes are processed parallelly in 3-D cube form. Experiments, including both simulated and measured tests based on a commercial mmW radar, prove that LFIST-Net is capable of reconstructing the imaging scene precisely. In particular, in near-field mmW 3-D holography tests, both numerical and visual results demonstrate LFIST-Net yields compelling reconstruction performance while maintaining high computational speed compared with MF-based, conventional CS-driven, and network-based methods.