A simple and efficient super-short-scan algorithm of fan-beam reconstruction for multiple circular trajectories: solution towards the truncated data

The sufficiency condition of the accurate reconstruction of the region of interest (ROI) in fanbeam tomography with non-truncated data was introduced by F. Noo([1]). When the detector does not cover the whole objet, R. Clackdoyle extended this condition of the accurate reconstruction of ROI in presence of the truncated data using virtual fan-beam method (VFB) [2]. In this paper, we are interested in the image reconstruction of the whole object from truncated data, since the whole object reconstruction is always preferred even with small detector, instead of the accurate reconstruction of only a region. We propose a simple and efficient super-short-scan algorithm for multiple circular trajectories to reconstruct the whole object from truncated fan-beam projections. This algorithm is validated by simulation studies.