DPI-SPR: A Differentiable Physical Inversion for Shadow Profile Reconstruction Framework in Forward Scatter Radar

Forward scatter radar (FSR) has emerged as an effective imaging modality for target detection, utilizing forward scattering (FS) signals to reconstruct two-dimensional shadow profile images of objects. However, real-world FS signals are inevitably corrupted by noise. Due to the ill-posed nature of electromagnetic inversion and its high sensitivity to noise, existing imaging methods often suffer from degraded performance or even complete failure under low signal-to-noise ratio (SNR) conditions. To address this challenge, we propose DPI-SPR (Differentiable Physical Inversion for Shadow Profile Reconstruction), an end-to-end imaging paradigm built upon the Secondary Wave-Source Response Field (SWRF). The core concept of this paradigm is to reformulate the imaging problem as an optimization problem of continuous and learnable SWRF parameters. To this end, we develop a fully Differentiable Forward Scattering model (DFSM). Leveraging this model, the proposed inversion framework integrates a robust logarithmic loss with physics-based regularization constraints, enabling accurate gradient propagation from observation errors to the SWRF parameters associated with the shadow profile. Extensive simulation experiments have been conducted to verify the effectiveness and robustness of the inversion proposed framework. The results show that our method achieves high-precision profile reconstruction directly from limited and noisy reference signals, even at an SNR as low as 8dB, setting a new benchmark for robust imaging in FSR scenarios.