Model-driven CT reconstruction algorithm for nano-resolution X-ray phase contrast imaging

The limited imaging performance of low-density objects in a zone plate based nano-resolution hard X-ray computed tomography (CT) system can be significantly improved by accessing the phase information. To do so, a grating-based Lau interferometer needs to be integrated. However, the nano-resolution phase contrast CT, denoted as nPCT, reconstructed from such an interferometer system may suffer resolution loss due to the strong signal diffraction. Aimed at performing accurate nPCT image reconstruction directly from these diffracted projections, a new model-driven nPCT image reconstruction algorithm is developed. First, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Second, a penalized weighed least-square model with total variation (PWLS-TV) is employed to denoise these projections. Finally, nPCT images with high resolution and high accuracy are reconstructed using the filtered-back-projection (FBP) method. Numerical simulations demonstrate that this algorithm is able to deal with diffracted projections having any splitting distances. Interestingly, results reveal that nPCT images with higher signal-to-noise-ratio (SNR) can be reconstructed from projections with larger signal splittings. In conclusion, a novel model-driven nPCT image reconstruction algorithm with high accuracy and robustness is verified for the Lau interferometer based hard X-ray nPCT imaging system.