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

The low-density imaging performance of a zone plate based nano-resolution hard X-ray computed tomography (CT) system can be significantly improved by incorporating a grating-based Lau interferometer. Due to the diffraction, however, the acquired nano-resolution phase signal may suffer splitting problem, which impedes the direct reconstruction of phase contrast CT (nPCT) images. To overcome, a new model-driven nPCT image reconstruction algorithm is developed in this study. In it, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Furthermore, a penalized weighed least-square model with total variation (PWLS-TV) is employed to denoise these projections, from which nPCT images with high accuracy are directly reconstructed. Numerical and physical experiments demonstrate that this new algorithm is able to work with phase projections having any splitting distances. Results also reveal that nPCT images with higher signal-to-noise-ratio (SNR) would 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 nano-resolution phase contrast imaging.