Cascaded Complex U-Net Model to Solve Inverse Scattering Problems With Phaseless-Data in the Complex Domain

The phaseless-data inverse scattering problems (PD-ISPs) are non-trivial due to their serious nonlinearity and ill-posed nature. The conventional methods for PD-ISPs can be categorized into single-step methods and two-step methods, where the first ones directly reconstruct the image and the second ones retrieve the phase and amplitude of scattered fields, and then reconstruct the image as the traditional FD-ISPs. However, the single-step methods correspond to solve higher nonlinear optimization problems and the two-step methods highly depend on the quality of the retrieved phase and amplitude information. To solve the above issues, we propose a two-step method with a cascaded complex U-net (CCU-net) model to solve the PD-ISPs in the complex domain. The CCU-net consists of two parts, that is, Phase Retrieval Net (PRNet) and Image Reconstruction Net (IRNet), where the PRNet recovers the phase and amplitude of the scattered field from the measured modulus of the total field and the IRNet takes the recovered scattered field as input to reconstruct the image. These two parts can be independently controlled and achieve joint optimization. Thanks to the strong nonlinear representation ability of complex neural networks, the physical relationship between the scattered fields and the images can be reserved and constructed. Several representative tests including both the synthetic and experimental examples verify that the proposed CCU-net in the complex domain has good robustness, generalization ability, and strong inversion capability when tackling high contrast scatterers and can also fulfill one-step implementation in real time.