FrDo-Net: a deep unfolding network for phase retrieval based on an adaptive fractional-domain physical layer

Existing deep unfolding networks for phase retrieval rely on fixed bases, rendering them prone to basis mismatch and energy dispersion when processing non-stationary light fields. To address this issue, we propose a fractional-domain deep unfolding network (FrDo-Net). By formulating the orders of the fractional Fourier transform (FrFT) as learnable parameters, FrDo-Net adaptively matches the optimal energy-focusing domain and integrates a Swin transformer to capture long-range diffraction dependencies. Furthermore, we design a differentiable pre-computed Eigen-decomposition-based FrFT (PCE-FrFT) operator to overcome computational and gradient bottlenecks, enabling the end-to-end joint optimization of the physical model and the deep prior. Experimental results demonstrate that under severe conditions, such as extremely low signal-to-noise ratios, FrDo-Net effectively decouples the desired signal from strong shot noise. Its reconstruction accuracy, texture fidelity, and noise robustness significantly outperform existing state-of-the-art algorithms.