Multi-contrast X-ray imaging simultaneously provides absorption, phase, and dark-field information, enabling improved visualisation of weakly absorbing tissues and unresolved microstructures. Conventional quantitative retrieval methods generally require multiple acquisitions, increasing delivered dose, acquisition time, and sensitivity to motion artefacts, thereby limiting their applicability in clinical and dynamic imaging settings.

We introduce an implicit single-exposure retrieval framework for the simultaneous quantitative recovery of transmission, phase-related displacement, and both isotropic and directional dark-field contrasts from a single reference–sample image pair.

The method locally exploits spatial redundancies of the structured illumination pattern within a sliding analysis window, reformulating the single-shot inverse problem as an overdetermined least-squares system. The sample image is expressed as a linear combination of the reference image and its spatial derivatives, allowing all contrast channels to be estimated from local intensity variations. A second-order diffusion tensor formulation extends the model to anisotropic dark-field retrieval and enables extraction of dominant scattering orientations.

Validation on a beryllium lens showed excellent agreement with the conventional ten-pair LCS reference, with SSIM values of 0.979 for the horizontal displacement, 0.987 for the vertical displacement, and 0.984 for the integrated phase. On carbon fibre tubes, the method simultaneously recovered transmission, displacement, isotropic dark-field, and directional dark-field contrasts. The directional tensor analysis preserved the fibre orientation in all six tube regions, with angular deviations remaining below   with respect to the multi-exposure reference.

The proposed framework reduces the number of required acquisitions compared with conventional directional dark-field methods while preserving quantitative accuracy across scalar and tensorial contrast channels. By combining compact instrumentation, local least-squares inversion, and directional tensor analysis, it provides a promising route towards low-dose, fast, and motion-robust multi-contrast X-ray imaging for biomedical and materials science applications.