Physics-aware measurement-supervised deep learning enables point spread function inversion in soft X-ray tomography

Soft X-ray tomography (SXT) is an emerging modality for whole-cell 3D imaging in near-native states. However, the effective spatial resolution is limited by optical artifacts characterized by the point spread function (PSF). To achieve optimal resolution via PSF inversion, we propose a measurement-supervised deep learning framework. Bypassing purely data-driven neural networks that are prone to hallucinations, we employ a measurement-supervised, instance-specific optimization strategy strictly constrained by a differentiable SXT formation forward model. The structural fidelity was validated using split-tilt Fourier ring correlation (FRC), ensuring the recovered high-frequency features reflect genuine specimen features rather than random artifacts. Our results demonstrate that this optimization consistently increases FRC resolution and enhances visual ultrastructural details across diverse biological structures. Furthermore, by recovering high-frequency features from sparse-angular projections, we show that spatial resolution can be maintained using only half the radiation exposure. This approach effectively compensates for the degradations caused by angular sparsity, providing a hardware-free computational solution to minimize radiation damage, maximize imaging speed, and overcome the optical and dosimetric limits of SXT.