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Phase-contrast CT (PCCT) is an emerging tool that has found numerous applications, including applications to preclinical imaging. There remains a need for reducing the imaging time in current PCCT. One approach to reducing imaging time is to reduce the scanning angular range in PCCT. However, accurate image reconstruction from data collected over a limited angular range (LAR) is challenging because it poses a problem of accurate inversion of the PCCT imaging model that can be highly ill-conditioned in LAR scans. In this work, we conduct an investigation of accurate image reconstruction through inverting the imaging model for LAR scanning configurations in propagation-based (PB) PCCT. We have developed a directional-total-variation (DTV) algorithm for image reconstruction from knowledge of the discrete X-ray transform (DXT) over a LAR for CT imaging. Observing the mathematical similarity between the DXT in CT and the imaging model in PB-PCCT, we develop and tailor the DTV algorithm for image reconstruction from LAR data in PB-PCCT. Results of our study show that the tailored DTV algorithm can yield image reconstruction with reduced LAR artifacts that can be observed otherwise in images reconstructed by use of the existing algorithm in PB-PCCT imaging. For a given LAR, it can be divided into sub arcs of LARs. We also investigate a scanning configuration with two orthogonal arcs of LARs separated by 90° , and observe that the two-orthogonal-arc scanning configuration may allow image reconstruction more accurately than does a single-arc scanning configuration even though the total angular ranges in both scanning configurations are identical. While boundary images can be reconstructed from data, we develop the DTV algorithm for reconstruction of the image, i.e., the refractive index distribution, instead of its boundary image from data in PB-PCCT. Once the image is obtained, the Laplacian operator can be applied to it for yielding its boundary image.
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