Robust iterative phase retrieval for x-ray in-line holography beyond the weak absorption and noise limits via dynamic physical constraints

Quantitative phase retrieval in x-ray in-line holography is crucial for imaging weakly absorbing samples, yet conventional methods suffer from the breakdown of weak-absorption approximation and severe noise amplification. To address these limitations, we propose a robust iterative framework integrating a multi-distance simultaneous algebraic reconstruction technique with dynamic physical constraints and adaptive gradient-weighted regularization. By employing a “hard-to-soft” constraint relaxation strategy, the algorithm mitigates stagnation in local minima, while adaptive regularization suppresses noise without blurring structural edges. Simulations demonstrate that the proposed method enhances the structural similarity index from 0.37 to 0.93 for strongly absorbing objects. Experimental validation on duplex steel yields a 13% improvement in signal-to-noise ratio while preserving spatial resolution (∼8.02 μm). This work provides a high-fidelity solution for phase retrieval beyond the traditional absorption- and noise-limits, proving highly applicable to complex, strongly attenuating materials and challenging high-noise imaging conditions.