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CSR-Net: A Novel Complex-Valued Network for Fast and Precise 3-D Microwave Sparse Reconstruction

Since the compressed sensing (CS) theory broke through the limitation of the traditional Nyquist sampling theory, it has attracted extensive attention in the field of microwave imaging. However, in 3-D microwave sparse reconstruction application, conventional CS-based algorithms always suffer from huge computational cost. In this article, a novel 3-D microwave sparse reconstruction method based on a complex-valued sparse reconstruction network (CSR-Net) is proposed, which converts complex number operations into matrix operations for real and imaginary parts. Using the unfolding + network approximate scheme, each iteration process of CS-based iterative threshold optimization is designed as a block of CSR-Net, and a modified shrinkage term is introduced to improve the convergence performance of the approach. In addition, CSR-Net adopts a convolutional neural network module to replace a nonlinear sparse representation process, which dramatically reduces computational complexity and improves reconstruction performance over conventional CS-based iterative threshold optimization algorithms. Then, we divide the 3-D scene into a series of 2-D slices, and a phase correction scheme is adopted to ensure that the whole 3-D scene can be reconstructed with measurement matrix of a slice. Moreover, an efficient position–amplitude–random training method without additional real-measured data is employed for the proposed network, which effectively train the CSR-Net without enough real-measured data. Extensive experiment results demonstrate that CSR-Net outperforms both conventional iterative threshold optimization methods and deep network-based ISTA-NET-plus large margins. Its speed and reconstruction accuracy in 3-D imaging can achieve a state-of-the-art level.