Quantitative imaging in synchrotron microtomographic (μCT) may be compromised due to the presence of strong artefacts. This study combines experimental data with X-ray simulations on GPU to correct linear attenuation coefficients in highly corrupted μCT volumes. We selected the scan of silicon carbide (SiC) fibres with tungsten (W) cores in a titanium alloy (Ti90/Al6/V4) matrix. The reconstructed images suffered from strong streak artefacts and phase contrast. The tungsten coefficients are underestimated by a factor of 2 (162 vs 342 cm-1) in the reconstructed μCT volume. SiC coefficients are overestimated by a factor of 2 (5.61 vs 2.74 cm-1). We registered CAD models by deploying a realistic X-ray simulation on GPU in an optimisation framework so that simulated projections matched the experimental data. The real experiment is numerically modelled, taking into account geometrical properties, beam hardening, impulse response of the detector, phase contrast, and photon noise. The weight of each type of artefacts is estimated for each pixel of the experimental images. The simulated artefacts are then “subtracted” from the experimental data. After this correction procedure, linear attenuation coefficients are comparable with their theoretical values. These results pave the way towards the use of high-performance simulations to correct actual experimental data.