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Inverse geometry CT(IGCT) employs source array and small detector, which raises requirement for new reconstruction method. Gridding-based method and direct FBP method have been developed for reconstruction, with degraded spatial resolution or computational efficiency. We recently propose a new FBP reconstruction for IGCT that merges the projections from all the sources to the final images using designed weightings. Although this method achieves excellent spatial resolution and is simple in practical use, the necessary zero-padding step that extends the detector to cover the whole scanned object causes increased time consumption in projection filtering and backprojection. In this paper, we propose an accelerated reconstruction for IGCT via derivative back-projection filtration(DBF). Compared with the proposed FBP reconstruction, the DBF reconstruction employ the same weightings, with only changes in the filter kernel, i.e., substitute the local derivative filter for the global ramp filter. Therefore, the DBF reconstruction formula could be obtained via the same derivation as in FBP reconstruction, and the computational efficiency is expected to improve since local filter poses no requirement for zero-padding. However, initial DBF reconstruction present images with strong streaking artifacts, so we further simplify the reconstruction to a stable implementation using the data redundancy. Simulation studies and phantom studies reveal that proposed method present images with comparable numerical accuracy and spatial resolution to the FBP reconstruction. In comparison with FBP, proposed method achieves acceleration with a ratio of approximate 7 for reconstruction of IGCT system with 9 sources.
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