Hybrid deep reconstruction for vignetting-free upconversion imaging through scattering in epsilon-near-zero materials

Optical imaging through turbid or heterogeneous environments, collectively referred to as complex media, is fundamentally challenged by scattering, which scrambles structured spatial and phase information. To address this, we propose a hybrid-supervised deep learning framework to reconstruct high-fidelity images from nonlinear scattering measurements acquired with a time-gated epsilon-near-zero (ENZ) imaging system. The system leverages four-wave mixing (FWM) in subwavelength indium tin oxide (ITO) films to temporally isolate ballistic photons, thus rejecting multiply scattered light and enhancing contrast. To recover structured features from these signals, we introduce DeepTimeGate, a U-Net-based supervised model that performs initial reconstruction, followed by a Deep Image Prior (DIP) refinement stage using self-supervised learning. Our approach demonstrates strong performance across different imaging scenarios, including binary resolution patterns and complex vortex-phase masks, under varied scattering conditions. Compared to FWM raw scattering inputs, it boosts average peak signal-to-noise ratio (PSNR) by 124%, structural similarity index (SSIM) by 231%, and achieves a 10 × improvement in intersection-over-union (IoU). Beyond enhancing fidelity, our method removes the vignetting effect and expands the effective field-of-view compared to the ENZ-based optical time gate output. These results suggest broad applicability for future biomedical imaging, in-solution diagnostics, and other scenarios where conventional optical imaging fails due to scattering.